You could have a virus doing it. What kind of antivirus are you running ? Boot the pc in safe mode and run this free download http://www.malwarebytes.org/mbam.php Make a note if any viruses are found and delete anything that it comes up with and see if the problem still happens.
I've never seen any software problem cause a PC to suddenly turn off - freeze, crash, restart or shutdown yes, but not just go off. If it is really turning off instantly then you have a hardware problem. PC's are cheap - buy a new one.
Is a power supply a power supply a power supply? I have two older pc's and could pull one of those and try it to see if it repeats the failure? Running today so far. I know I need a new setup but I'd rather hunt up the guy that built this one and have him do it again since he knows what the hell he's doing. Thanks again....