I'm going to throw out a lot of suggestions here and hope something sticks.
I guess you could uses MBM or Speedfan to check the PSU voltage levels your BIOS reports under load, but that can be very imperfect. I suggest it just in case there are wild voltage swings (you seem to have already checked temps). Otherwise, buy a $10 multimeter and check the PSU's rails (+12V, +5V, +3.3V) yourself. That's what I ended up doing when my PC starting flaking out on me, and it turned out it wasn't the PSU but rather wonky drivers.
Maybe try disabling C 'n Q, just to eliminate as many variables as possible (in this case, from the software side)? Or try reseating your CPU HSF, RAM, and check that the 7800GT's HSF is in working order? While you're down there, check that no caps have burst or are leaking, on both the MB and vid card.
The inability to restart for a minute seems to make faulty RAM less likely, but it probably wouldn't hurt to run MemTest overnight.
Or just put that $10 toward a new PSU? An ATX 1.3 unit might not take kindly to the +12V focus of your new MB and GPU.