That machine I was working on for my friend Harold turned out to be fried. I did get it to turn on once, but that was it. It shut down at one point, then never turned back on. Tons of debugging, involving disasembling the entire machine and cleaning it, proved fruitless. I even tried plugging the mother board into a separate power supply, and also plugging the hard drive into another computer. Neither worked.
I think it was all the dirt and grime inside the case and on the components, including the motherboard, which was to blame. Here's some hints and a video from CNET which discuss this.
Seems like the dirt inside, if it gets on the case, can actually create a short in the board, and then the board and the whole system short itself out. I'm pretty sure that's what happened.
Also, here's a page detailing a similar computer problem in a machine shop.