There are two mini 6-pin power cables on the board in the MacPro. When I had a GTX 680 (official EVGA for Mac version) there were two 6-pin power cables on the GPU itself. Needed to use two mini 6-pin to standard 6-pin power cables to power the GPU.
Your GTX 680 is a 4GB model, so it's not an official Mac version. It's either a straight PC card, or it's been flashed/modified by someone to "make" it a Mac card.
What brand & model is the GPU?
What are the power requirements?
Are there two 6-pin power slots on the card? One 6-pin? One 8-pin? One 6-pin + one 8-pin?
What port/connection are you using to connect to your monitor?
The card appears to be an ASUS GeForce GTX 680 DirectCU II NVIDIA - 4GB
It has two 6 pin power slots both of which are connected. It's connected to the monitor with a VGA cable. I'm informed by the person who sold me the machine that the card is NOT flashed, but I can't verify that.