|Your specs list leaves a lot to be desired - "some random Gigabyte motherboard" - you don't know? And how do you allocate RAM to a game?|
Have you confirmed the monitor(s) is working correctly by trying it on a different system or with a different video card? Is the GTX 560 TI a new addition or have you had it for a while? Do you have a decent quality power supply that's capable of handling the load?