I am thinking it might be a bad CPU. I had a similar problem with an old Dell. I can't remember the detail symptoms. But if the CPU is overloading the PSU, it will try to start and shut down. The fans not operating would be another clue that the power is being shorted. If you pull the CPU and it stays on and the fan runs - though obviously nothing will happen - then that is the answer.
Troubleshooting anything else on the MB is not for the faint of heart.