PC is randomly shutting off
Solution 1:
You could install CPU-Z (http://www.cpuid.com/cpuz.php) to monitor your voltages while the machine is on. Perhaps your PSU has a low tolerance for line voltage variances. You could purchase a P3 Kill-a-Watt from Newegg (about 25USD when i bought mine a few years ago). This has many other uses besides monitoring line voltage. There also PSU testers out there but those can be pretty expensive. I would first try CPU-Z then try switching in a known-good PSU.