Have you installed the latest AMD drivers? Are they both plugged into monitors? For Windows to recognize them they both need to be plugged in, or have "dummy plugs".
I keep hearing this over and over and over again, but in a simple setup like this it is no longer required since a long passed driver update, I don't recall the exact revision but I think it was pre-12.1
There is nothing plugged into 2 of the 3 graphics cards in my system and I operate cgminer just fiiiine.
6870 --> two duplicated DVI->HDMI outputs
5970 nothing connected
5750 nothing connected *sometimes a HDMI to my TV for when my esteemed motherboard decides this card should randomly be the primary display device while showing the boot process
OP, can you see both cards if you load something like GPU-Z ??