There was a yellow flag on the Coprocessor, but I've downloaded and updated the latest ATI drivers for my motherboard since then (since the ZIP files above)- (edit: and it then detected the coprocessor / updated the drivers successfully) and I just rebooted after yet another BSOD. All of a sudden, at random, my mouse/screen will freeze, the system hangs for about 5 seconds, then it goes to this screen (taken with my phone):

It just sits there, at 0%, forever. And no dump was created, C:\Windows\Minidump folder still doesn't exist.
Note: This problem started happening prior to installing Win8... I noticed it started occurring regularly a few weeks ago to my Win7 64 install- even though I didn't change any hardware or even install any new software, for that matter... I can't figure out what might have triggered this happening. I've tested the HDD and memory and everything comes up clean.