My PC is driving me mad! It was working fine one day, then when I turned it on the next morning there was a whirring noise (coming from, I think, the PSU fan) and it turned itself off after about 15-20 seconds. Nothing appeared on screen.
It sounds more like your CPU fan which is not reaching its correct running speed and does not reach the threshold speed required.
This would cause the PC to shut down, a more likely scenario than a faulty PSU Fan.