PC Shuts down during bootup with Ultra or Corsair

I have an HP Media Center PC. AMD64 X2 5000+, 3GB RAM, running Vista 32-bit. It has been upgraded with three additional HD's and a 9800 video card (with PCI-E power input) and initially with an Ultra 750W PS. This worked fine for a few months but then started randomly shutting off on it's own. Installed my spare OCZ 700W PS and all works fine. Replaced the PS with another Ultra 750W PS and it consistently shut down when Vista got to the desktop and began loading apps. Replaced the Ultra a second time with new and it exhibited identical behavior to the one it replaced. Because the OCZ works fine and the Ultras did not, Ultra commendably replaced their 750W PS with an 850W model. Unfortunately, same story -- shuts down on bootup after the login screen. I figured there must be something with the Ultra brand that was not suitable for this computer, so bought a new Corsair 750W PS which I've read is one of the best brands. However, it does the same thing as the Ultras. Only the OCZ 700W works in this computer, though I'm concerned about having no backup if it should fail. Any ideas why the other supplies won't work? I've tried unplugging the data hard drives and DVD drive to reduce load as a test but the behavior persists.

 

The side has been off during this problem with a fan blowing on the innards. No change. As I mentioned, it also happens when the drives are disconnected, and it shuts down before fully booted up -- hardly enough time to get hot. Any other ideas?