There is another thing it could be, which happened to me this past year. Somehow the processor and its heat sink became slightly separated, and as such, the heat sink was no longer doing its job. Because of that, my processor's auto-shutdown feature would kick in and suspend power from going through the system.
You'll know if it's this when you go back and check it later. If it turns on later when the chip is cool, then this is a possibility. If it shuts down again after a minute or two and won't turn back on until the chip cools again, it is a likely candidate for what's wrong.
I thought it was power supply too, when it happened.
-Matt