I've got an HP m7760n that is nothing special. Every few days or so the computer hangs and the screen goes crazy with pink lines across the screen and flashing colors (you can still see what was on the screen, it's just all flashing and the computer doesn't respond).
I guessed that the system was overheating but various factors make me think maybe that's not it. I've added fans which hasn't helped including a high powered fan that blows across by the video card. It doesn't seem to matter the ambient temperature in the room (could be cold or quite warm in the room) and it will work fine for several days and then one day it will be hosed.
When my friend's computer did that, we noticed that the fan on his gfx card had stopped. I replaced that fan with an old fan that was still good.
Unfortuneatly, the gfx card still failed a couple of months later.
First thing I'd do is get a can of compressed air and blow the dust out of all of your heatsinks, and PSU (CPU, GFX, and MB). Check to make sure the fans are still spinning, and if it's an actual video card (not onboard) download rivatuner and adjust the fan speed (could still overheat if there is a dead area in the case).