Crashes unless I underclock my GPU.. Help narrowing down the problem?

Wasn't sure whether to post this in BSOD section, or here, but I'm pretty sure I've narrowed it down to my GPU, so I posted here.

I've been battling BSODs ever since I built this rig. It is my first one, so I only vaguely know what I'm doing. I thought I was overheating, but my temps were waaayyy too cool for it to be that (like, 60C). I was getting random crashes though when my system was under load, that I kept under control by tabbing out of my games and letting the system idle for a while to "cool down".

I finally decided to use MSI Afterburner to underclock my GPU. And low and behold, I haven't gotten a BSOD since.

Now, my question is, knowing that underclocking fixes my errors, what is the problem? I don't think the card itself is at fault. In the midst of trying to fix this issue, I actually sent it back in and got a warranty replacement. Same issue. Is it a problem with my power supply? If so, it must mean it's a faulty unit, because the model is more than capable of running my system. Is it something else I haven't thought of? Thanks for the help.

Specs:
GeForce GTS 450 GPU
Coolmax CUL-650B Power Supply - 650-Watt
4GB Ram - Transend, 2 x 2GB
ASUS M4A785-M Motherboard
1 TB Seagate HDD
32 GB Patriot SSD for Boot (this is a new addition to the system though, problems started long before I installed the SSD)

A few things to check. One, make sure the new GPU is fully seated and locked in place. Make sure that you have the right power connections connected (1 or 2) to GPU and fully seated. If possible try not to use an adapter on the power connections. Make sure you have the latest driver installed for your GPU. Make sure your GPU is installed in the right PCI slot. Check to make sure that your fan is working on your GPU and see what temps it's reaching while in use. SpeedFan and GPU-z are good apps for that.

Checking your specs on GPU, your minimum wattage is 400 and you have a 650 watt PSU, so your good there.

Did you try overclocking the GPU to see if the problem got worse or became more frequent? There is (should be) an auxiliary power connector on the motherboard for the GPU near the GPU slot. Did you plug that one in as well? Typically it is a four pin receptacle.

Were you able to take a multimeter to the PSU leads to at least confirm proper voltage amounts? Testing for load is much more difficult unfortantly.