Human-vampire hybrid wakes up from hibernation that started in the late 30's and finds that world has changed.
What kind of knowledge from the 30's would be best starting point to learn computers & networking?
The best starting point would be knowing about Turing Machines. Alan Turing thought these up in 1936, so your human-vampire hybrid could have learned about these shortly before entering hybernation.
In case you are not aware, a Turing machine is basically an abstract version of a computer. It's a theoretical device that can compute anything that can be computed. Computers are really just fast Turing machines with fancy outputs.
If your hybrid had heard about Turing machines, waking up from hibernation and seeing computers would, instead of being a "what in the world is that" experience, be a "wow, they actually made them" experience.
Math. It's the basis for computer languages and would give a good starting place to learning modern languages.
The first low level programming languages where created in the 40's, and high level languages in the 50's.
So the vampire would not have had any experience or knowledge of computers in the 30's.
Knowledge of math would at least give a background in abstract logical thinking and make things easier.
My great-grandfather headed an Electrical Engineering department from 1946-1956, just as the important transitions into electronic processing were being made and WWII computing technology became unclassified. During his tenure as chair, he purchased the university's first computer, REAC 100, and hired some professors to develop on it.
His background was in electrical engineering and acoustics. He wrote papers on such things as electronic hearing aids, communication theory, and bridge circuits during the 1930s. This would probably be the best applied background to make the transition into computational sciences.
Computers are all about... well... computing. So first option would be some kind of profession that deal with collecting, collating and computing data. Preferably so in an very strict and organized manner according to certain procedures / algorithms.
The 1930s had the battle grounds where the formal mathematical definitions of computation were hashed out, there's a random internet find timeline here with all the popular names, but I think that's pretty irrelevant. Most computer users today don't go for a mathematical understanding, even advanced users.
But the hundred years or so leading up to that had enormously relevant inventions. Your wealthy and curious Vampire could have known about the existence and some-level of workings of these computer precursors:
From there, they are close to knowing about encoding letters as code symbols, representing symbols as electric signals, reconstructing electric patterns into useful output, about recorded and stored information (paper, punched cards, pressed audio cylinders), about decomposing sound into frequency blocks. The jump to encoding sound measurements as code symbols, storing words on pressed cylinders, representing text characters with lots of very small lightbulbs (pixels), using those lightbulbs as dots to represent pictures like in a newspaper print, keyboards as electric typewriters, and tiny control circuitry is a matter of disbelief of scale or practicality rather than disbelief full stop.
Cherry picking these examples really makes digital computers seem inevitable, doesn't it? I'll say the best thing your Vampire could know from the 1930s era was enough of these things: telegraphs, keyboard style interface for writing with tele-typewriters, the existence of signalling codes, and the use of electricity to power and control things (switches, lights, machine tools, sewing machines, beepers, indicators, dials, readouts) that it seems reasonable that the combined effects could give rise to modern computers, that computers are surprising only in scale, not in principle.
The real mental jump problem is 'stored program computers can do things' and I can't think there's any reasonable way a person from pre-computer era will be able to grasp that intuitively without closely following up-to-the-minute math developments. But signalling codes, electricity as a controller, and feeback systems in general, give as good a background as they're likely to get.
And the mention of WWI is that the Vampire would have lived through it, and would have seen both the desperation of the participants, the burst of technological development (foot warfare to tank warfare, no planes to aircraft, more and more submarines, etc). and could maybe have seen economic problems of 1930s Germany and stresses in Europe. Therefore learning about WWII would not be much surprise that the scale was bigger, the weapons were more deadly, the war was longer, and the technology boost was starting from a higher place and pushed harder and faster.
Library science. It helps people to think in terms of storing and finding information, which is what "the net" is all about. Perhaps a bit of mathematics on top, graph theory.
Somebody already mentioned Turing, but that has to be number one. The second thing to pick up on is Claude Shannon's work. In 1937, he wrote a thesis demonstrating that electronic circuits could simulate all the constructs of Boolean algebra. Given that mathematicians had already shown that the rest of mathematics could be built up from Boolean algebra, this pretty much lays the basis for electronic (rather than electromechanical) computing. He did a lot of significant work in the 1940s, as did Turing, but that's outside the scope of the question.
Another thing to look into would be Polish decrypting techniques of the late 1920s and early 1930s. These techniques led to the construction of the Bombe, a device that was replicated at Bletchley Park in Britain during WWII.
It's probably worth learning the differential analyzer, designed by Vannevar Bush. This was an analog computer, and therefore could be a distraction from the mainstream of the future, which would be digital. But it would give you a handle on the power of simulations. Knowing that, plus the knowledge that digital simulations would eventually come along, would be helpful.
And, of course, there's Herman Hollerith who devised a scheme for storing census data on punched cards in 1890. His company was bought out by a sales man for NCR, who gave the company a new name, "International Business Machines".
IBM would remain in the punched card business until 1954, when it decided to take over the computer industry, more or less.
And, of course, the work of the first programmer, Ada Lovelace. Her work had been around for almost a century in 1930, but it was still ahead of its time. She practically invented software engineering as a separate discipline from equipment design, and previewed the development of artificial intelligence.
If you want some background on other innovations available in 1930, take a quick peek into The Innovators a book by Walter Isaacson. He outlines progress in infotech from Babbage through Google. The first couple of chapters should give you lots of material.
A lot of this stuff was old by 1930, but learning it at that time would put you ahead of the curve.
In addition to math (especially binary), Morse Code would give a good understanding of how computers communicated with each other.
Edit: My apologies. I think Morse Code is a bad example. Perhaps I should have said the telegraph and Baudot code. Baudot would introduce your vampire to the concept of 5 bit character encoding so the concept of 7 or 8 bit ASCII (or just bits in general) wouldn't be a drastic leap for the vampire.
The sort of mechanical computing people were doing back then was things like this: https://www.youtube.com/watch?v=s1i-dnAH9Y4
There are useful precursors; Morse code is a binary code he might know. He would not have used a calculator, but might have used a slide rule, which requires him to know how to convert numbers to logarithms and back for multiplication and division. (That’s still a technique electrical engineers sometimes use under the hood to implement those operations in hardware.) The layout of modern keyboards is the same as mechanical typewriters, although most men of his time would not know how to use one, because that was a job for women. Telephones existed, but there is literally nothing about a modern phone he would recognize, not even the concept of reaching people by dialing only digits without talking to an operator, or of leaving a recorded message instead of getting a busy signal, or that it’s possible, much less expected, to call someone up when you or he are not at home and rude to show up unannounced. Movies existed, but not television or VCRs, and you couldn’t watch video in color any time you wanted and pause or go back whenever you felt like it.
Science fiction wouldn’t help him much. Isaac Asimov two decades later was still imagining that the engineers in the far future of his space operas would carry in their pockets unimaginably more-advanced slide rules. As for social changes, if anything, science fiction of his day was behind the times.
The part of the curriculum that’s changed the least would be pure math, but there are still a lot of huge differences. He wouldn’t have learned to add or subtract the way old people today think of as “traditional,” because that’s the New Math introduced in the 1960s. Proofs were something he learned in geometry class, not something done in high school algebra, a lot of his time would have been spent memorizing techniques to do by hand calculations that are now always done by computer, it wasn’t generally accepted that the foundation of mathematics was ZF set theory, and nobody has even heard of the Rule of Three.
He’s essentially a foreigner in the modern world. People don’t walk, talk or dress like he expects. Especially women. Everybody wants to be on a first-name basis. Radio exists, but he wouldn’t recognize anything on it. Newspapers exist, but nobody reads them and even the comic strips are tiny and crude. If anything, computer programming is the one aspect of his daily existence at a university today least likely to cause him culture shock: the Internet and video games would be weird, but he has no expectations about them to violate, and computers are possible to completely understand.
Step 1: Look around for some days to get an idea of current world and society also set a camp/safe-house somewhere.
Step 2: Keep doing step 1 and start asking people about "security" and "measures" taken while doing some crime and learn how not to behave strange by using some hypnotic-power you have.
Step 3: Get an idea of "how people are educated", specifically in that field using your hypnotic-powers.
step 4: find a university and track bright students and ask them to help you by giving some tuition at their home/rooms.
Now, if your vampire is this much smart then he will have a safe-house, rough knowledge of modern society and a bright friend who will be willing to teach him computers and will be far less suspicious.
Definitely understand that whatever computers (and embedded computers in appliances, cars, industrial control etc., and ANY "digital" electronics) do these days would have always been done by something mechanical or electromechanical (relays, electromechanical counters...) back then, not by something built with early electronics (or only using these in very select places, eg. a photocell amplifier)- these were expensive and large, and reserved to tasks that required dealing with mostly analog (speech, video), fast (an electromechanical system will usually be hard pressed dealing with things happening in less than 1/1000th or maybe 1/100000th second, or signals above 1-100kHz ... non-electronic telephones,loudspeakers... are among the faster electromechanical devices) and weak (a radio signal from an antenna cannot operate a relay or motor usually, a signal from a microphone will not drive a loudspeaker directly, even though electromechanical amplifiers did (rarely) exist) signals/events.
Telephone exchanges (that already existed at that time) are a good example of an electromechanical system that handled "digital" tasks (and they were still built new that way well into the 1970s in some countries). Somebody understanding how these worked could understand a lot of computer logic by seeing it as a very fast acting telephone exchange that used electronic switches instead of electromechanical ones.
Electronic controls on eg. a tape recorder or household appliance are a good example of something that only became economic to do electronically in the 1980s - earlier designs used complex mechanics to do these things instead.
By the 1930s there were devices whose operation was controlled by complex electrical circuits. Push Button Elevators are a good example.
Relay Logic was being used to control sequencing of machinery:
large relay logic circuits were employed from the 1930s onward
See also George Stibitz
... studied the correspondence of statements of symbolic logic with binary relay circuits while a graduate student at MIT. Shannon wrote his graduate thesis (published in 1938) on that subject ... Clearly the idea of using relays to implement binary logic was common in the late 1930's.
The seeds of digital computing were well planted by that time.
I suggest "Maths".
The proof is that Maths was my whole/only background, before I was introduced to computers.
Someone (a mathematician) who's trained to accept algebra (e.g. "x = y + z") can extend that to computer programming: it's symbol-substitution.
Perhaps for a similar reason I think that alternatively some of the earlier 'boffins' might have been linguists: bilingual or multilingual, whether with modern languages or classics (Latin or Greek). Training for multiple languages, translating from one language to another, might be another kind of good preparation for a programmer (i.e. it's symbol-substitution again).
I guess that (personal) character/disposition is important too. A programmer needs to be willing to read the manual[s], spend time alone with the machine. If you can only get your kicks from interacting with other people, maybe you won't be willing to study this kind of stuff.
FWIW I learned the elements of networking at my first employer too. The historical terms you'd want to be familiar with are "circuit switching" versus "packet switching" (and maybe "multiplexing"). I presume that most modern networks are packet switching.
My career as a programmer started in the early 1980s: before personal computers were common, and before programming was a frequently-used option at university.
I'd hardly used a computer by the time I left university. I read a couple of programming language books (Fortran and Cobol) from the public library when I was 12 or so -- and having read them I thought that, "maybe when I grow up I'll work for a company big enough to actually own a computer, to program".
Nevertheless (in spite of the fact that most graduates didn't have experience with computers) my first employer (Bell) employed 100s or 1000s of programmers. I think they figured that people who could learn Maths (at university) could learn programming, if they were hired and given a computer terminal.
I think I learned, given:
I think he would not keep up with what the world has now, even in computers (seriously, my dad is 65 years old and he doesn't know how to turn on my computer.). Lets give this as a example.
Your computer puts up the welcome screen.
You have a 600 year old vampire, with a knowledge of computers equaling that of a child, I'll bet he would say "Thank you" to the computer screen (and how about if you describe to "open a window")
The basic knowledge which he must have is the the basics, turning on the computer, what happens when it turns on, what happens when windows pop up, and what to press or not, which in the 30's does have that kind of system, but is not as complex as our current computer system.
If you will, give your vampire a calculator first.
Railroads. He will understand the concepts of bandwidth, power, routing and speed. Having him be an expert vampire railroad baron would be advantageous for your story.