I used to blog about problematic computers that came in the shop. Haven't done it in a while, but today I had two odd balls that came in about the same time.
The first one wouldn't turn on unless the side of the case was open. In fact, when you put the side back on, it would turn off. Weird, but ultimately was the power supply. When the case was put together, it would move the wires in such a way that the power supply would short. I thought about actually finding the short in the wire, or likely in the molex connector, but in the end it was easier and better for the customer just to replace the power supply.
The second one was a bit trickier. The customers power supply, motherboard, CPU, and ram would all post out side the case. But in the case it would turn on for a moment, then shut back down. I thought for sure it was a short somewhere on the motherboard while it was in the case, but I couldn't find anything. I tried a different power supply, motherboard, CPU, and ram in the customers case, and it did the same thing. It finally dawned on me the only thing different between being in the case and out of the case, besides the case, was the atx power switch. Low and behold, replace it and everything worked fine. Second time in my career as a PC technician have I found the actual power switch to be the culprit. In this one's case I did a continuity test with a multimeter to find the switch was always on. Which explains why it would come on for about ten seconds and turn off no matter what hardware was in the case.