Black screen & hang when playing video

The PC in question:
Gigabyte GA-B75M-D3H mobo
Intel Pentium G870 CPU
ATI Radeon HD7770 (MSI Computer Corp. R7770-2PMD1GD5/OC)
Kingston 4GB 1333Mhz DDR3 RAM (single stick)
Windows 7 64 bit

I built this PC a few months ago as a gaming/media machine connected to our HDTV via HDMI. It plays 3D games and runs general apps just fine.

When playing video (.mkv, x264 .mp4, xvid .avi, or .flv) the machine will randomly hang on a black screen with buzzing audio. The computer is unresponsive and requires a reset. This happens with VLC player and BS player. There's no pattern that I can tell: sometimes we'll get through a movie or episode, but rarely. Sometimes it crashes 30 seconds into a video, other times 30 minutes. It doesn't seem tied to a particular part of a video: it'll hang at one place, then we'll try again and it'll play through that part fine but hang somewhere else.

I've uninstalled all drivers, run DriverSweeper, and reinstalled fresh drivers. I've turned off any kind of extra video processing I can find in VLC's options and in Catalyst Control Center. I've tried playing video from a USB stick as well as the internal hard drive.

I've checked my temps for both my CPU and GPU card and I'm never anywhere near high temps or high load when playing video. The computer works much harder playing games, and it does that fine. I've run a Prime95 stress test and Memtest and everything checks out.

I've gone to Gigabyte's site and downloaded all the latest drivers. The one set I can't install are the VGA drivers, it says "Your hardware doesn't meet the minimum requirements for this software." Which is odd. Maybe it's expecting a i5 or i7 instead of the Pentium? Could that be the problem? The Pentium is on the compatibility list for this mobo.

Any ideas for things I could try, or suggestions on how to pinpoint the problem, would be GREATLY appreciated. I'm hoping I'm missing something obvious. This is my third build and my other two run great with no problems. Heck, this one runs great except for playing video! Argh.