Well, I installed a Corsair GS700. A few problems are gone, but now I'm having new ones...
Basically, whenever I reconfigure my RAM (as in change which stick are in which DIMM slots) and clear my CMOS, the computer will POST and boot into Windows (so stably, in fact, that I can run stress tests and game without a hitch). But as soon as I shut it back down, I'm unable to even POST until I change around my RAM again.
I'm messing around with 2 sticks of 2gb 1600MHz (running at 1333MHz) Ripjaws and 2 sticks of 4gb 1333MHz. I have a hard time believing that they're all dysfunctional.
Any thoughts? I'm absolutely stumped. Temperatures are all normal (CPU maxes at 60C in Prime95, GPU runs around 40C in Crysis 2, ambient temps are just a few above room temp).
And again, all settings are stock, since the BIOS gets reset every time I change around the RAM.
Oh, and I've resat the CPU twice (as other sites have advised me to do), as well as tried a different one. Which seems to narrow it down to the graphics card (?) or the motherboard.
Finally, it turns out that obscure error that the computer was having (that I never wrote down) turned out to be a Hyper Transport Sync Flood Error, which seems to be consistent with the white lines appearing on the screen earlier.