Computer shuts off had bad power supply

I'm trying to fix a friends computer she said it just shut off and would not turn back on.

What I have done so far

• Used PSU tester on PSU, failed, replaced PSU. That got it to turn on for a few seconds then shut down.
• Opened case, saw heat sink was dusty and clogged.
• cleaned and reinstalled heat sink with Arctic Silver. Then it started running a little longer it would partially start up windows and crash when the pointer appeared.
• Went into the BIOS to check the CPU temperature it seemed OK at 33-35 degrees Celsius, froze in the BIOS.
• BIOS froze and shut down a few more times eventually that stopped.
• Ran memtest86, passed.
• Boot safe mode, worked.
• Boot into an ubuntu live cd, worked.
• Boot regular mode, worked once, now shuts down at pointer again.
• Boot diagnostic mode, still shuts down at pointer.
• removed the video card, stayed on, but no way to tell if it actually booted all the way.

I'm stumped. I'm not sure if it is hardware or software, because it was freezing and shutting down in the BIOS screen, but the RAM passed, the CPU heat sink isn't real hot, the hard drives sound OK. I also tried shorting the motherboard power switch pins instead of using the case switch, but that didn't seem to matter. I'm waiting for another friend of mine to get home so I can borrow his AGP video card and test that. Any other suggestions, bad motherboard maybe?

 

This suggests that it's not related to OS.

I'd check for bad caps on the motherboard, barebones troubleshooting, test with a different PSU ...

 

Already checked the caps they all look good, I think I'll try pulling the motherboard to make sure its not shorting on the case. I got it to boot all the way once and then restarted it to see if it was fixed and it shutdown again. Its starting to do it earlier now, like before it gets to the welcome screen.

 

Turned it on this morning and it's back to shutting off after a few seconds, so I'm starting to think its a HW problem.

 

Sounds like it's time for the barebones troubleshooting then

 

I got it all out on cardboard now and it still shutting down, but that was with the case switch I'm going to try with screw driver now.

 

OK it shuts down with a screwdriver, so its not a case problem, I guess I need to find another PSU to try.