computer shuts down & reboots on its own

I am working on an old computer, 98SE,AMD 300, 256mb RAM,
CD burner, 10 gig HD. Plenty of room left on the HD. Everything works fine until it suddenly powers off, then reboots. It is subject to do this with nothing running, while starting various proggies, while running various proggies, etc. Then again, it may run all day with no problems. No consistent way to make it happen, no new software loaded, Adaware, Spybot S&D, and AVG have been run to be sure (or at least fairly sure) it is clean. Does it with nothing hooked up but a monitor, keyboard and mouse and nothing running but system stuff, explorer and systray (use EnditAll, not just ctrl-alt-del). Any help appreciated.