maybe the power supply is dead

Similar problem here. It is not because of the SATA, but because that SATA needs power or say that extra power knocks the PSU dead.

Maybe you can try to remove video card (if there is any), or use another PSU to try.

Several of my computers got this same problem ... well, because I've used the same PSU to play around. Finally I dumped it! The world is quiet then.