While I've never repaired (or even seen) a Micro-Kim, I do repair quite a few vintage computers and video games.
Things from this era usually hold together pretty well if they're stored somewhat decently.
However, we have reached the point where RAM and EEPROMs are dying of old age. My troubleshooting list usually goes like this:
1. "Thou shalt check voltages"
2. "Thou shalt check your oscillator"
3. Probe CE/OE on the RAM+ROM, make sure they have flanks. Also, check one of the low address-lines on the ROM (not A0 in 16bit machines though), to make sure the CPU is trying to read something.
4. Probe every data-line on the ROM. Make sure there's no dead ones.
5. Same for the data-lines on the RAM.
If all that checks out, _actual_ troubleshooting starts.
