Hell, I'm not even sure we can make a computer that actually lasts 100 years.
I'm pretty sure we can. I have a 40-year-old calculator that is still working just fine.
Still, I was probably too ambitious when I said "computer". I was thinking more that we can't make a PC or server-style computer that would actually last 100 years, while in regular operation.
Also, 1980s calculators have much, much fewer moving parts than today's computers. They don't have any kind of active cooling, they don't go through rapid heating and cooling cycles, they probably have three orders of magnitude less electrical components than a modern PC.
For me at least, all of the PCs I have had so far have had a few electrical components giving out after at most 10 years (usually some condensers leaked).
In fact, it would not surprise me a bit if you could run a Raspberry Pi Zero for 100 years.
I wouldn't even be convinced then that we have the technology today. Any repair system would necessarily suffer from the same kinds of failures.
Might as well ask Archimedes to send a probe.