Easy causes could be loose chips (give a solid push with your thumb on any socketed ones) or a marginal power supply (try with no cards (especially the disk drive card) installed). Harder causes could be non-socketed chips failing. That's bad because most of them are special purpose in the IIe, and not generally available at your neighborhood electronics vendor, and would have to be de/re-soldered anyway.

Anyway, rip everything out that's not bolted down, squish the chips, and see what happens.