My first instinct on this is power supply. I see similar behaviour in PCs fairly often. I had a Sun server do the same : damn thing ran for four years straight, had to shut down one night and it refused to come back on. Replaced the power supply, came back up just fine.
Unfortunately, sometimes a bad PSU can take out an otherwise good board, too :cry:
I am in the process of replacing my desktop Amiga PSUs with mini-ATX units. Well, I would complete this process if AmigaKit would start selling 2000-ATX adapters! ;-)