Help with diagnosing dead PC

This machine has been working perfectly on a daily basis for over a decade. It hasn't moved or had any hardware, software additions to it recently. Friday it booted up fine. Saturday it started to boot, then instantly stopped. A few seconds later it started to boot again, and again instantly stopped. So basically stuck in a loop.
I have stripped everything off, removed motherboard from case. Now just motherboard, single stick of RAM, and CPU and cooler. This behavior still persists.
With just the 24 pin ATX connector attached all seems OK, but this fault loop starts as soon as I attached the 8 pin CPU connector.

I have tested the PSU with one of them cheap PSU testers.
I have removed, reseated CPU, cleaned and reinstalled CPU cooler.
I can't see any problems with the motherboard: no bulging caps, no signs of burning or anything like that.

What else can I do to diagnose the problem?
Could it still be a PSU issue (I don't have a spare to test with)?

Any thoughts appreciated. This machine has several SAS HBAs installed, connected to four 8-Disk SAS RAID5 Arrays which contain my archive.
That's all backed up of course, but the last thing on earth I want to do is restore 96TB of data...