DisplayPort not working (GTX 670 + i7-3770K)

When you plug the cable in, do you switch the monitor's input to Display port?
Also, when it's plugged in via Display Port, does it show up under the Nvidia control panel?

I switch the monitor to DisplayPort. It's shown in Windows too (when I try to set resolution it shows me 2 monitors), but I can only set the resolution and see picture on the one running on DVI (is the same monitor with 2 different cables  )
I'll check inside the nVidia control panel too.
What bothers me is that it's not only in Windows, but I can't see the UEFI too when I turn on the PC (even before I didn't even had OS installed).

Maybe not the best solution since it isn't solving the problem of the displayport not working but why not use DVI cables for both of your monitors? That's assuming you have two of the same monitor... Or use an HDMI to displayport adapter and see if the signal is picked up. Could be a bad port on the monitor or a bad port on the video card.

There are also DVI to displayport adapters you could try. Just wondering why you want the display port to work so bad if you only have two monitors and thus only need two connectors on your graphics card which has four ports... Granted if you wanted to add more monitors in the future, it would be frustrating. One other thing to try might be a different displayport cable since it could be a dud... Can't really rule anything out and failures do happen. If you have access to another monitor and/or another computer/device with displayport, you should see if it works on that.