You've added a lot of stuff, I was thinking the PS is overheating or being taxed. I have an old MDD that has add on USB and firewire cards and 4 HDs. If I use a beefed up video card I need to unplug a HD or two to keep it from randomly shutting down.

Are all the fans working? If you leave the case open, possibly with a small fan on it does it shut down? Maybe you need a PCI exhaust fan or two to pull the heat out of the case.