Also, after scanning some other things on Tom's Hardware, I found out my 7950GT uses ~60W at load. So theoretically 450W - 60W = 390W. I highly doubt my other hardware is using that much. But as I am not a certified computer technician, I'd like some verification if at all possible.
You need to know how many amps are supplied combined on the 12 volt rails. I would say that yes, the PSU would be the first thing to suspect. Can you list the amps/wattage off the sticker on the side of the PSU, if it has one? PSU's that come with the case are not usually spec'd very high. And if it came out of a server case, it is likely not capable of suppling enough amps on the 12 volt rails for the video card you have.