Well it'll either be PSU, Motherboard, or failing that the CPU itself.
If you have any spares to swap in/out do that. If you don't have spares, and don't want to take it to a shop (where they will have spares to test with), then only option is to buy one part at a time until the problem is solved.
I normally do the latter, and use it as a chance to upgrade.
It would be great if someone came in with a definate answer, but chances are the options above will be the result.
I'd start with motherboard and/or PSU, and CPU as last resort OR take it to a competent shop.