Thanks for the help, but after I posted that I did a little more digging. Turns out that the video card tries to power up when the machine gets plugged in, and every time I plugged it in, I let a little more of the magic smoke out. I used my eyes to trace where the smoke was coming from, and sure enough I found some blown ICs on the graphics card. Put another card in and viola! IT WORKS!!!! Something in the short circuit on the GPU card must have been dragging the power supply down or something…
Thanks for the help, but it was not the power supply! What an odd one!