Last night I diagnosed a System 80 that didn't work more times than it did. The problem? A faulty pin 4 hole in ROM socket 2.
This is the third machine of mine where a faulty socket has caused an issue. I've had similar problems with my Kaypro II and Commodore PET.
A common technique when faced with a newly acquired machine that doesn't go is to reseat all socketed chips. This is a good idea, but must be done really really carefully otherwise it can damage old sockets. Far from curing a problem it can actually be made worse. This probably happened on all three machines mentioned above, as they certainly went through a chip reseat.
Anyway, something to be aware of.