... Random Shutdown Problem

What is my next troubleshooting step?

My build:
Antec 300 Black Illusion (4 fans)ATX Mid Tower
Biostar TA790GXB3 AM3 AMD 790GX ATX Motherboard
G. Skill Ripjaws Series 4GB 240-pin DDR3 SDRAM DDR3 1333 (PC3 10666)
AMD Phenom II X4 955 Black Edition Deneb 3.2 Ghz 4 x 512KB L2 Cache 6MB L3 Cache AM3 125W
Western Digital 500GB 7200 RPM 16MB Cache SATA 3.0Gb/s 3.5"
Asus DVD Burner 5.25”
Antec Earthwatt 500W Continuous PSU

- No cross firing
- No over clocking
- no RAID
- no sound card
- no video card

My problem: Random shutdowns with no error messages and no warnings
I've been using system since 5/2010 without complaints, but 4 months ago my PC turned off after 3 hour of use, and from then, started to shutdown randomly without any pattern. Sometimes I'm away from the system when it shuts down. It does it most consistently when I open two browsers using Flash for online games. First I ran MEMTEST+86 to check the memory sticks and everything was fine after 6 tests.

I tried to use Prime95 In-Place test to measure CPU temperature, but system shutdown less than 1 minute into test. Not sure about the results – found 2 new text files:
Prime:
V24OptionsConverted=1
WGUID_version=2
StressTester=1
UsePrimenet=0
MinTortureFFT=128
MaxTortureFFT=1024
TortureMem=8
TortureTime=15

[PrimeNet]
Debug=0

And Local:
OldCpuSpeed=3520
ComputerGUID=d55212b32a8d1f59f0614d05d1f7d845

Anywhere to find performance info. in PC? Should I just replace the thermal compound in the CPU? Is the motherboard the problem? Could it still be the power supply?