If this is an 'old' mother board: There probably is a switch, or a jumper(to remove), that will default the mother(system) board back to factory settings.
This has a dual BIOS, there is two chips. It will automagically copy the backup to the main chip if it gets corrupted. There is also a switch to manually switch between them. There is also another button to manually induce copying the backup.
From reading my understanding is one way to corrupt the bios is overvoltage, there is factory turbo mode supported by the Intel chip I have for overclocking and in both cases it was on.
I think what happened here is when the main bios got corrupted the PSU failed at the same time. I can't even get it to turn the power light on now so I'm fairly confident the old PSU is in fact toast. When I installed the new PSU what I failed to realize is the BIOS was manually switched to the backup so it was never copied to the main BIOS chip. I must of corrupted the second BIOS. It's the only conclusion I can draw that makes sense since I was able to boot with new PSU without any issue.
I would try to reload the BIOS from the web.
Once a computer gets to this state it can't be reloaded AFAIK, you need functioning BIOS to reflash the BIOS. That is why there is two chips, If I had it switched to main BIOS when I installed the PSU it would have copied the good backup over the corrupted copy and I'd be back to two functioning copies.