Sounds a little more like the motherboard. It could be the power supply as well, but since the fans are spinning up and lights are coming on, the power supply is at least operating in some
fashion when you're having the problem.
It could really be any number of things, though. To troubleshoot, I'd probably start by unplugging everything non-essential to boot...like all drives, all but one stick of RAM, all fans, etc. Then plug things back in one at a time (try switching to the other sticks of RAM by themselves to test each individually).
If the problem isn't consistent, it's going to be a bit harder to pin down...I'm not sure what to say about that other than it will likely get more consistent as time goes on.