First of all I would tend to agree that it sounds like a PSU problem. I know you don't have a second computer but if you have a friend that would let you swap PSU's I'd try that. I've also seen ram cause this but not very frequently, so testing that would be something I'd try. And for something far out in left field change powerbars or ever wall socket that your are using. I encountered this on a computer and only managed to figure it out when I took it home to test only to find it started with no problems but wouldn't at her place (although there were issues of random reboot and occasionally not starting, leading me to replace the ram, mobo and PSU since it was a new build.)
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