Mac Pro early 2008 doesn't boot anymore

I got a Mac Pro early 2008 2x 2.8 quad-core for 12 years now. A few weeks ago, it stopped booting after 5 seconds. I restarted it and it was ok. But the problem came more and more often the next days, and today it just doesn't boot anymore. It stops after only 2 seconds. I've noticed that the CPU LEDS 5 & 6 flash in sync one time at the very end, when the fans stop with a last 'clic'. I tried everything I could do before posting this question, I mean unplug all hardwares, cleaning, and I followed the very complete answer from @monomeeth Boot fail diagnosis

When I press the DIAG_LED, I got only the LED 2 on. So I don't know if the problem comes from the Logic Board or from the PSU... hope it's not both :(

I'm about to order a used PSU for trying, but I'd like to be sure. The noob question is : if it's a PSU trouble, why the computer was able to start correctly sometimes ?

Thanks in advance for your precious help !

The new PSU did the job ! The EFI led is still off but everything works fine now :)