I had a similar problem about a year ago with my PC. Got me puzzled for a while because the fans kept kicking in for a brief second or two then seemingly restarting in a loop. I realized that I hadn't plugged either the power cable to the GPU or CPU, can't quite remember which it was. As soon as I fitted that in it booted up perfectly fine.
I'm suspecting PSU, CPU, or mobo as primary. What I would do if I were in your case is reset the CMOS as a few have suggested. Failing that I'd basically disconnect all the cables (both power and data) to the optical drives, spare HDDs (or all in fact), PCI cards, USB peripherals, extra fans, etc. Basically strip it down to a bare system so you can rule out most things. Then try playing with the combination of PSU, mobo, CPU, GPU, KB+Mouse.
Let us know how you go with that.