I think that might be it. I did buy from a bargain PC company and it was four years ago. It has two fans at the back under the power supply, and one at the side fanning the video card and whatnot. I'll get pictures if you want. I have had noted problems in the past with the video card artifacting, which I ended up having to replace.
Currently I'm keeping a regular ol' desk fan running at high at the opened side of the case to determine if that's the problem. Upon a suggestion from a friend, I've also switched the power cords for the monitor and PC. So, I guess if the monitor randomly shuts off or the PC keeps running that's it.