Does sound a bit like some kind of memory issue, though this symptom can be caused by many different things. Intermittent IC sockets would be my next guess.
You might get a few more clues using DiagROM. Give that a shot first as it's low cost and easy. You'll probably need a null modem cable to look at the initial serial data output on a second computer.
Failing that, I'd have to connect the board to my real-time system debugger to see what's going on. I'm still doing plenty of Amiga repairs, though international freight price has increased a lot over the last year or two. Drop me an Email if you get stuck.
http://amiga.serveftp.net
