Try this to confirm my suspicions. After the computer has been off for a while (1+ hours), turn it on and let it sit in the BIOS screens for 10-15 minutes. Then exit the BIOS and boot normally.
This sounds like an issue with the PSU (when it is warmed up, it works fine). I would suggest replacing it with a good quality PSU (Antec, Corsair or Seasonic).
I am going to try this tomorrow later tonight or tomorrow as the PC is my wife's work PC. I will let you know what happens.
Edit: Tested this, let it sit for 15 minutes at the BiOS utilities for 15 minutes and no BSOD. Thanks a bunch, Ronintexas!