ATI Mobility Radeon HD 4670 shutting down computer

I have an Acer Aspire Z5610 all-in-one desktop. Windows 7 Ultimate 64bit.

History:

I was getting a blue screen, generally when multitasking and streaming video going. A friend suggested a video card driver upgrade, which did in fact resolve that problem. A few months down the road, the computer would just suddenly shut down. No blue screen. Found and installed an updated driver (8.920.0.0 date 11/9/2011), but didn't resolve problem.

The only thing that seems to prevent the shut downs is to change the "theme" to "Windows 7 Basic", without any HD wallpapers. Additionally, moving windows around is not smooth and remnants of closed windows stay on the screen occasionally.

Found some threads here that mentioned a conflict between Intel chips default video driver and the ATI driver, but only the ATI card shows up in the device manager.

I just assume it's the video card or driver because changes in how the graphics are displayed seem to effect the shutting down. Some have suggested it's the RAM or mother board.

I am not an advanced user, so any suggestions you can offer will be greatly appreciated.

Ivan the SoSo said:

Have you tried blowing out the vents on the system?

Yes. Several times.

It doesn't appear to be an overheating problem, because it can even happen on start-up. Right after booting up, if I happen to open 2 programs at a time, it will shut down. This doesn't happen, however, if I have the "Windows 7 Basic" theme. It only happens when I have one of the other themes with the HD wallpapers.