I had a similar issue the other day, just out of no where motherboard refused to boot. Turned out my 8-pin ATX wire had died. I tried a new PSU and everything worked fine so I started going through the 24 pin then the 8 and 4 pin and found it was the 8 pin ATX that was dead for some reason. Replaced the wire and all works now.
I would try with a separate PSU just on the 24 and 8 pin and see if you can get to BIOS. If you don't have a second PSU. Try moving the 8Pin wire to another slot on the PSU or if you have a modular system try different wires.
Beyond this, then you are looking at CPU issues. Check for bent pins. One or two bent pins can do things like you are describing.
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