I don't buy it; a C64 is simple enough that you could work out the functionality of most components by trial and error and then work back from first principles. You'd measure 5v TTL, and under a scope you'd see the 1mhz binary signal. From there, 74 series chips on the board would probably be the first to be identified, simply based on inputs and outputs. And once you did that, and knew that this was a NOR gate or whatever, you'd pop the top off, look at it under microscope, and start to work back from your knowledge that this had digital logic and you'd figure out what the _function_ of a transistor was even if you didn't know what it is.

The RAMs and ROMs would be fairly trivial to figure out, as well.

You might not learn the manufacturing process -- that really did take a couple decades of material science and physics advances. But the principles of the machine would be clear. And then you could take the knowledge of that and scale it to the electronics components available in the era. You'd definitely have a head start simply knowing that these things were _possible_, and getting a boost on knowing how a computer could be structured.

They can probably figure out that the little plastic things either store data or perform computation. By process of elimination since wires, resistors, capacitors, PCBs can all be analyzed for their properties.

Given that knowledge they can try breaking those pieces of plastic apart to see that it's a housing over some sort of ceramic core. Using spectroscopy and chemistry you can figure out what that core is made out of. Now you know what mix of chemicals allows for really high density data storage and computation.

Using x-rays and microscopes they can figure out that the little ceramic die has some sort of structure etched on it. Maybe remove tiny pieces to see what different parts/layers are chemically composed of.

Now they know that there's something interesting about certain elements deposited on top of silicon using some sort of etching approach. Early transistor research was already well along (and had been patented already in the 20s) so it's likely they would have made the connection. Given all that you can start brute forcing industries and ideas around those materials.

They would see the "© 1982" on a chip and although it would be incredibly futuristic (35+ years in the future!), would at least know it was likely to be created by humans. Whether they could work out how on earth you place such incredibly tiny components onto a sliver of silicon is interesting. If the person taking the computer back in time mentioned the word "photolithography" I suspect they would have been able to make a pretty good guess.

I'm pretty sure you're wrong. People are very good at pattern recognition. You don't need to understand the physics to check lots of combinations of inputs and deduce what this black box do.