Do the GPU fans spin when you turn on your computer?
Yes, the fan turns on. As a way of checking if perhaps my VGA to DVI adapter was broken, I also connected my desktop to my TV with an HDMI cable, and the TV wasn't getting any input either. Do these circumstances mean it's safe to say I just got a bad video card?
It seems to be seated correctly, and unfortunately I only have one 6 pin PCI E cord so I cannot try a different one to my PSU.