Zapping the PRAM is usually one of the first steps in troubleshooting. You might want to pull the drive and any upgrades. If there is a network card in there, pull that. Try pulling the harddrive and booting from a floppy. If it reboots off the floppy, you might have an issue with capacitors where they drop out.

I seem to recall that caps fail in weird ways where they will take a while to start up, or they will require running and then restart just to get them to work. or they will run fine for a while, and then all of a sudden you get stability issues.

Not sure what to tell you, but start with zapping PRAM and pulling all items except the board and a floppy. that will tell you more than guessing