Edit: I do not have the best technical understanding of computers so some of my terminology may be misused. I guess a simpler way to imagine this hypothetical computer is one whose overall performance (how fast it can run an arbitrary program) can scale with power supplied infinitely.
Say a genius mad scientist has built a computer sporting a single-core CPU with a potentially unlimited clock rate - the more power you give it, the faster it will perform operations. If you power it with a potato battery, it will be as fast as
my laptop a potato; If you power it with a nuclear power plant, it will be proportionally faster by X times (where X is how many times more energy the plant produces than the potato); if you built built a Dyson Sphere for the computer then it will still make full use of all the generated energy.
Edit: A comment has mentioned the problems that might arise from trying to dissipitate huge amounts of energy through the computer. So, in consideration of this, assume that the computer simply "eats" all the energy it uses by magically teleporting it to a distant corner of the universe.
We assume that the mad scientist has figured out some way to circumvent physical limitations on clock rate. I imagine there is a point where a CPU with a clock rate of ten septillion trillion ghz would break the laws of physics (is there?), but we pretend that isn't an issue.
I'm not sure how the CPU performance should scale with power, so I leave that to you to decide. Please try to be reasonable.
Furthermore, I am splitting the question into two separate scenarios:
The CPU can write to and read from RAM instantaneously and RAM is unlimited.
The CPU can read or write to RAM as fast as we can achieve today, and the RAM is the maximum conceivable size of one we could manufacture today.
I guess with this, factors like hard disk read and write and hard disk storage size also come in. Again, I'll leave these details to you, but I'd appreciate if answers were varied!
P.S. The mad scientist has since died in your standard mad-scientist-type accident and there is absolutely no way of reverse engineering the technology he used to build it. The computer is, and forever will be, one of a kind.
Having established the computer's RAM/storage related capabilities as you see fit, what could be potentially done with it? If a malicious hacker group obtained it, how much harm could they do? If one country had it, what advantage would they gain?
Bonus: if all of humanity miraculously came together and decided to pool all the world's resources to maximize the computer's benefit to all of humankind, what could be achieved? Are there major issues we could solve, or advancements we could make with a potentially ridiculously fast computer?