With the HDD's connected when you power on do you hear the drives spin-up?
If you have case fans/HDD's etc spinning when you turn on the PC I would say it's not the PSU. In my experience PSU's either die completely or short intermittently meaning you'd be able to boot but then you'd suffer random reboots.
I'd be leaning towards a dead mainboard, if possible test your CPU in another PC to narrow it down.