13.5V is high - not sure exactly what would cause that (power supply issue?). Usually the problem is the opposite with voltage too low. I think most (maybe all) of the chips would run off 5V.
At this point, it really could be anything wrong with the logic board.
May be worth taking a close look with a magnifying glass on backside to see if there are any broken solder joints, and on the component side to look for broken or corroded traces or components.
After that, I'd go through the diagnostics in a systematic way. For example, follow the algorithms for "dead sets" in the Larry Pina repair books.
Good luck!