Strip everything out of it except the mobo, PSU, VGA, CPU and RAM and try to boot. The last step is to try to build same on some card board and check for a short, but I don't think that's your problem.
You may just have a bad mobo or possibly a bad PSU. Try using the PSU to Power a case fan only, to see if it will stay running. You may need to power a hard drive as well, some PSUs need a 5V load. That won't guaranty that the PSU isn't failing under a higher load but it is a good indicator.
If it's the mobo, then get yourself a P4x series. The 680i is plagued with problems.nVidia, fix the 680i chipset! Petition