My first thought when reading the question was that you were describing a sudden end to human life followed by (or at the same time as) an alien landing. Could the alien species reverse-engineer our technology and benefit from the remnants of our culture? (I can imagine scenarios where the surviving aliens are not the ones who built their ship or understand the alien tech...either another species on board or a group of people who were culturally isolated from the builders...perhaps it's a penal colony.)
Then I re-read it and realized that you are asking about earth evolution. The problem here is time.
- How long would it take for another species to evolve to the point
where they could understand written language, use computers, operate
machinery, etc? We need evolution both of intelligence and of their
bodies to be able to do these things, though many species could
physically manipulate some of our tech right now, if they knew how.
- How long will our tech last such that it's usable in some way?
Looking at the evolution of primates, it appears that the line that created humans split off about 7 million years ago. We got crude stone tools about 2.5 million years ago. Around 100,000 years ago, we got sophisticated tool-making (while this number is in dispute, it's not going to be off by a million years). Scientists argue that these early humans had the cognitive ability for modern tech, but the culture wasn't there yet.
So the question is, how long will it take a species to go from basic tools to modern human cognition? Many species (including several non-primates and even non-mammals) already have the ability to make tools. How long would it take them to make the transition? Assuming they have any incentive to do so...
I don't know the answer, but it's likely at least 10,000 years and probably at least 100,000. And that doesn't even take physical issues (eyesight, manipulation of objects, body size, etc) into account.
So how long will our tech last while waiting for this?
Books: Certainly hundreds of years, maybe even a couple thousand under the right conditions.
Writing on more durable materials: Some will endure 10's of thousands of years (we have cave paintings, Egyptian carvings, etc). Assume some might make it through evolution if we accelerate the timeline, but there won't be very much there. No manuals or histories or anything substantial.
Computers: Tens or hundreds of years as a huge maybe. As for "the internet," that is a huge network of computers with many components that require maintenance. So no way would that last more than 100 years. No chance of evolution happening in this timeframe.
Buildings: These would last for a while in the beginning, and animals could make use of them. But eventually, they'd all fall apart. Will the Skyscrapers Outlast the Pyramids? A few buildings will make it thousands of years, but climate plays a big role too. I would say that buildings left over after 10-100 thousand years would not be a factor...they would not be usable or influence the development of technology.
Garbage: Some, sure. We have garbage from tens of thousands of years ago and artifacts from earlier as well. But mostly it's buried. Over time, landscapes shift. We don't generally have access to things after that amount of time without doing serious archeology.
As I see it, you have two choices:
Put human technology and artifacts into a time bubble so they are artificially preserved (think the magic of Sleeping Beauty, or use alien/future tech).
Bring in almost-human aliens who have the cognitive ability already but who need some time (a few hundred years maybe) to really figure out the technology part.