Well, I think you can factor out the PSU, since it still gets the power to beep
(this is not a solid diagnosis BTW.)
You could try taking out one of the memory thingies if you have more than one to see if it's the memory. It's highly unlikely all of the memory died at the same moment.
It it still fails, I'd guess it's the mother board. Though you can not be 100% sure unless you actually replace it. The PSU is still a candidate and may be cheaper to try to replace first.