It always amazes me, that there are so many different ways for a power supply to fail (or in this case, partly fail).
This is a computer I've worked on previously, and at the time, the power supply would behave strangely when it was initially plugged into the wall. Ie, once plugged in, it would take about 15 – 25 seconds before the PC could be started. It seemed like a slow-charging capacitor, but since the PSU didn't cause any other problems, and since it worked well otherwise, I just ignored it.
Since then (about 3 months ago), the PC has started to randomly power off and reset.
So I replace the 500Watt PSU with a 450Watt I carry around as a spare.
Now the PC can start as soon as power is applied to the PSU, & the random resets have gone.
A complete sudden failure is much easier to diagnose than a random, "works 99%" failure.