Broken E&MM Spectrum Synth

I’d say one thing is to replace any electrolytic caps that show signs of leaking or bulging.

For the keys that don’t work it’s just a matter of finding and fixing bad connections and/or cleaning bad switch contacts or replacing switches.

For the envelope generator, now that you know where to find the schematics, you know which components are part of the EG and you can look for problems there. There are two envelope generators, are both malfunctioning? It’s hard to see how a single fault could break both. If one’s working and the other’s not then, after checking pin connections to make sure nothing’s shorted, you could try swapping the 3310 chips to see if that swaps which EG is working. (That’s assuming the chips are socketed of course.)