Hey everyone, I'm new to the forum and I've come bearing gif... troubles

.
Basically, I bought a new system recently and it just came in a couple of days ago. The first thing I noticed when I got it was that it didn't have the PSU that I ordered. In place of it was a really cheap Xion 700watt PSU. Well, I was ticked but I figured I'd test it out with the hopes that it would work well enough. It seemed to be running fine at first and I was even able to get through the passmark benchmark test about 3 times without a hitch, although strangely enough, I started with a score of around 1,660, but when I ran the test again it was in the low 1400s. I couldn't really figure out what would cause a drop in performance like that but that was only a minuscule problem compared to what happened next.
I fired up warhammer online to give it it's first test with gaming, and after only about a single minute or two of playing, my computer completely shut off. Being a novice to computers for the most part, I started searching around for the causes of complete shut downs and, sure enough, everything was pointing at the PSU. Anyway, while I was browsing I saw someone mention the furmark stability test so I decided to give it a try. At first, it ran ok for awhile, with the temperature peaking at around 92 or 93 degrees (btw, is that temperature supposed to be of the Video card, or the PSU?). But when I hit "space" to start the fur rendering it was almost like I hit the off switch or something because my computer almost instantly shut off again.
I haven't messed with it at all since because I don't want to screw up any of the Hardware. Everyone I've talked to said that it's almost certainly the PSU causing the problem, but what I don't understand is, why would the "fur rendering" stage cause the shut down? When I tried it on this computer (my old PC), the "fur rendering" stage caused my temperature to drop a ton, so wouldn't that mean that the PSU is under LESS stress in that stage? In other words, does it make sense that the "fur rendering" stage causes the shut down? I don't know much about your program so I have no idea of the mechanics involved in the stability test. If someone could set me straight about this, I'd really appreciate it.
As for the steps I've taken so far, I've already had Ibuypower (the company I used, but likely never will again) send me a new PSU (a Corsair TX750W, which I was told was pretty good), and I should be getting it tomorrow. I know nothing about installing a PSU but I was told it's fairly simple as long as you follow the wires of the old one and replace them accordingly. I'm hoping that will do the trick, but I can't help but be a little worried.
Anyway, the "Too Long Didn't Read" version - Does the "Fur rendering" portion of the stability test cause more of a strain on the PSU? Does it make sense for my computer to shut down on THAT part, and not the part before it?Thanks in advance for any help you guys can spare. I could really use it.
-Sean
(Btw, here are the specs in case you guys are wondering)
Case Nzxt Alpha Gaming Tower Case - Black
Processor Intel Core 2 Duo Processor E8600 (2x 3.33GHz/6MB L2 Cache/1333FSB)
Motherboard [SLI] Asus P5N-D -- Nvidia nForce 750i SLI Chipset w/7.1 Sound, Gb LAN, S-ATA Raid, USB 2.0, IEEE-1394, Dual PCI-E MB - EPU Technology
Memory 4 GB [2 GB X2] DDR2-1066 PC2 8500 Corsair Dominator Memory
Video Card NVIDIA GeForce GTX 275 - 1.7GB - Single Card
Power Supply 700 Watt -- Xion Power Supply - SLI Ready
Processor Cooling Coolermaster V8
Video Card Brand === High Performance === EVGA Brand Video Card Powered by NVIDIA
Primary Hard Drive 500 GB HARD DRIVE - [16M Cache, 7200 RPM, 3.0Gb/s]
Optical Drive 22X Dual Format/Double Layer DVD±R/±RW + CD-R/RW Drive - Black
Sound Card 3D Premium Surround Sound Onboard
Network Card Onboard LAN Network (Gb or 10/100)
Operating System Windows 7 RC
Flash Media Reader/Writer 12-In-1 Internal Flash Media Card Reader/Writer - Black