Do you own more than 1 computer?
Take the PSU and put it in another case. It's a bit of work, but far less work than yanking the entire motherboard, CPU, cooling fan, heatsink, cables, etc.
If it works like a charm in another PC, it's not your PSU.
If it's not the PSU, my biggest suggestion would be to shop around for a new motherboard.
(after swapping out the CMOS battery, of course)