These are the worst kind of problems to have. They can be power, or heat, hardware, or software related. Nailing it down can take some time, or you can get lucky, right off the bat.
Most motherboards, today, have a monitor page in the BIOS where you can monitor the voltage levels of the power being supplied to the motherboard. Start there. All the voltage levels should be within +/- .2V or the optimal level and should be rock steady.
Let it sit there, for a few minutes (5 minutes is plenty), from a cold start, and watch the levels.
Listing the components here might tip off someone as well.
Good luck.