I don't understand your problem. When you have 1 power cable connected to the GPU it works fine and when you have 2 it doesn't?
Intel i5-3570K @ 4.7GHz | MSI Z77 Mpower | Noctua NH-D14 | Corsair Vengeance LP White 1.35V 8GB 1600MHz
Gigabyte GTX 670 OC Windforce 3X @ 1372/7604MHz | Corsair Force GT 120GB | Silverstone Fortress FT02 | Corsair VX450
I had a bit of trouble understanding too, but to confirm. Have you tried BOTH power plugs in, and ONLY the DVI from the card (No motherboard video connected at all)