Hey I'm Isuru and have a problem that you might help
I have foxconn mars motherboard, It is 3.5 years old now
It has following problems,
1. Some times PC not power on, mobo led bulb works, but not booting
But after 2/3 days its working normally, Once starts it working completely normally, No over heatings, 45-49 C processor temp, 70-72 C while games playing. (71 C normal in Core2Quad Kentsfield cpu)
2. Some times processor identified wrongly as Core2Due, but after restart it shows correctly as Core2Quad.
3. Computer booting and no display, after 4-5 seconds it is restarting and still no disply and keep restarting. But it is works fine when I re-install the battery,VGA or Ram cards until I turn off the PC. When next day same problem continues. (This problem arise when PC is shutdown around 10-12 hrs, boot completely normally otherwise.)
4. Some times take too much time to pass the POST screen.
Well your problem is an eratic behavior so if it were the power supply the regular way of checking it wouldn't work because it would show that the psu is working so the only way to test your psu is with a power supply tester that will test each voltage that the psu has. The 3.3v , 5v and the 12v and you could also check it with a voltmeter so you may need to bring it to a repair shop to have them test it.
The other way to test it is if you had another psu that you could put in your computer and see if the same issues would come up. But not everybody has a spare psu or another computer you can take one out of for testing.