Dying or Inadequate PSU?

I think I may need to get a new PSU, but before I order one I'd like to get a second opinion.

My specs:

Rosewill Xtreme Series RX750-D-B 750W
ASUS M4A79XTD EVO
AMD Phenom II X4 965 rev. C2 (140w)
2x A-DATA Gaming Series 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1600
2x 500GB WD Caviar Blue
Radeon HD 5850
SoundBlaster X-Fi ExtremeGamer

This is a new build and I've been having a slew of problems with it after I upgraded. I initially only had one set of the ram kit (2x 2GB) and a 320MB 8800GTS which were upgraded with an additonal memory kit and a 5870.

My system hangs, BSOD's, or restarts, or even completely shuts down when under heavy system load (I.E. gaming or running stress tests like Prime95). System hangs after maybe 5 seconds running Prime95. Occasionally there will be a continuous high-pitched noise coming from my speakers, but I'll still be able to perform tasks or other times it will hang. After a series of crashes my system won't POST or will hang in bios or in mid boot.

I have done no overclocking and have actually underclocked my RAM from DDR3 1600 down to 1066 MHz with 7-7-7-20 timings because my CPU's IMC supposedly can't handle 4 sticks clocked at 1333 MHz very well. I've tested all sticks in memtest86+ individually, in single and dual channel with no errors. I only had one time where it would produce errors and it was after a series of system crashes and had 16 errors within the first 2 mins, but that was the only case in which I had errors.

The problems seem to dissipate for a while when I disconnect my PSU's mains and re-seat the hardware on my motherboard.

I really hope the PSU is the culprit, being that it's the cheapest component to replace. -prays-