Okay, so I've been fighting with this for a while now and have finally exhausted all of my resources that don't require me to go spend a bunch of money on a theoretical guess.
So here's the issue, my desktop (a self-build) works for a little while, then the screen freezes, the sound stutters in place (like a scratched CD) for about 2 seconds, then joins the display in the state of non-functionality. The only way to bring it out of this state is with a hard-reboot. Even then, it may start to load up and then freeze until I shut it off and let it sit for a while.
What makes me suspect the graphics card or mother board is that it tends to happen when I'm doing something graphics intensive (which could also mean I'm spiking the functionality of the machine in all aspects) But my lean towards the graphics card is brought on by the fact that in my most recent tests (taking everything apart and reapplying thermal compound to both processor and graphics card), when I rebooted the computer, it ran for all of about three minutes and froze up. When I pulled the computer apart, the entirety (not just the heat sink) of the graphics card was hot enough to burn me.
So, any suggestions before I go buy a new graphics card on a guess?