Desktop restarts/dies at random, seems to do choking restarts

Hello,

My boyfriend has a ibuypower desktop we've been upgrading throughout the past 2 years. It was running fine even long after the last upgrade until the power supply went completely dead. We just got a new power supply RMAd to us (same 750 corsair, should still be ample voltage.) Admittedly I have pulled the whole PC apart in the interim cleaning out dust and cat hair and putting in new thermal paste. I put it back together, ran the system stability tester I normally used with parted magic linux to heat it up and let it spread and cool back down. It never seemed to reach anywhere close to critical temperature and the bios now shows it at most in the high 20c. It will restart now at any phase of bootup and in some cases just completely power down, while sometimes it seems to sputter on and off rapidly as if it was choking. My next step is to fully breadboard it but so far I have pulled the power and reset cables to ensure its not a faulty switch. I haven't seen a computer restart like this before so I'm looking for more advice.

Thanks

Derek