I realized that a bit after I said it.... I hate to say this, but, after setting up the rig in my apartment, and trying something out(that was not part of your suggestion, Nastyman, sorry), it is fixed, and I did not know how it is fixed.
While I was setting the rig back up, I thought about trying something out, so I plugged in my DVI connector into the NVIDIA card and sure enough, no signal. So I shut down the computer and unplugged the DVI from the NVIDIA card and plugged it back into my main 6870. I start up the computer again, log in to Windows, and after booting up(since I use a mechanical drive still, it takes a while), Windows tells me I have updates. I check the updates to see what they were, and one of them was for an NVIDIA display driver.....I then opened up the device manager and lo and behold, it said it had a third VGA controller..... So I guess I somehow managed to either not seat the NVIDIA card all the way in, or I seated it in such a way that either some or none of the PCI-E pins between the motherboard and the card connected(I don't know if that could possibly happen).
tl;dr The card miraculously fixed itself, or by something that I inadvertently did.