New System with BSOD Problems - Help Please!

Hey, I just built a new computer for myself and my girlfriend, and hers is getting BSOD randomly every couple hours, even when only downloading from the internet. When playing Lord of the Rings Online, the game itself was crashing every few minutes, but the computer wasn't.

The specs are:

RAIDMAX HYBRID 2 RX-730SS 730W ATX12V V2.2/ EPS12V SLI Ready CrossFire Ready Modular Modular LED Power Supply

ASUS M4A78T-E AM3 AMD 790GX HDMI ATX AMD Motherboard

AMD Phenom II X3 720 2.8GHz Socket AM3 95W Triple-Core Black Processor

G.SKILL 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10666) Dual Channel Kit Desktop Memory

Western Digital Caviar SE WD3200AAJS 320GB 7200 RPM SATA 3.0Gb/s 3.5" Internal Hard Drive

EVGA 896-P3-1255-AR GeForce GTX 260 Core 216 896MB 448-bit GDDR3 PCI Express 2.0 x16

It's running Vista x64.

After the BSOD, I ran the vista troubleshooting, which said it is a hardware problem, and that I should check the hardware.

In Prime95, after letting the computer run for only about 7 minutes on the "Blend" mode, the third core had an error and stopped running. It said

"FATAL ERROR, Rounding was 0.5, expected less than 0.4
Hardware failure detected, consult stress.txt file"

It's only reaching temperatures of 42'C for the CPU when the third core faults, and voltages look fine.

In the small FTTs mode of the test, all three cores passed the first little iteration of the test.

In the large FTTs mode of the test, the second core had the same fatal error after 9 minutes.

My computer and hers are completely compatible, so I'm wondering what and how I should test first. Would taking out pieces of her computer and replacing them temporarily with pieces of mine be a good method to test hers? If so, which should I do first? I was thinking of taking out and testing the RAM first. Then CPU. Then PSU and video card. If it's not any of those, it must be her motherboard, right?

Thank you so much for your help. I wish my computer could've been the unstable one!

CPU-z is showing the ram at the manufacturer specs 9 - 9 - 9 - 24, but I'll go into BIOS and double check. And I'll download memtest86+ too.

Turns out if you give Prime95 just 15 minutes, all three cores will have that error. Joy.

And yeah, in retrospect, I've decided the raidmax wasn't the best choice. Too late now, though!

If the RAM voltage and speed are set correctly in the BIOS then Memtest86+ should run with 0 errors. I'd RMA the RAM if you even get 1 error with the RAM timings/speed/voltage set to the manufacturers specs.