Enebias: The cable was in the graphics card the whole time. Unfortunately, I cannot test it in another machine...
Actually, I would be glad if my GPU was indeed defective: at least I would know where the problem lies!
Funny how silent Nvidia fanboys are now, usually you'll get things like my condolences if you said "I bought an AMD card"
On topic, there are various things that can cause your problem. You might want to plug/unplug the cables again. Might be that your cables are messed up and not giving the gpu enough electricity. You light have a faulty gpu, try to contact nvidia support or try to post on their official forums and see if they can help you out.
Also you have done all the cleaning stuff (meaning uninstalled in safe mode, downloaded a registry cleaning software to delete old registries etc) but if you go to safe mode with network does the gpu still freezes for you?
Also is your mobo and psu compatible with the gpu? Does it get enough watts etc? Did you use the pci-expres slot and used the right 6 pin cables? (not those 4+2 pin cables). Also during replacement, did you push the gpu hard enough? (you should hear a clicking sound when it's in the right place) Didn't you touch any other hardware like the ram sticks, might be that the ram sticks got lose or something.
And can you monitor the temperatures with gpu-z? Do the fans work properly? Might be that your gpu gets heated really fast... So there are a lot of things that can cause your gpu to malfunction like that. So good luck, I know how irritating that is. If nothing works, add me on some steam chat or on fb and I will assist you on chat i I can :)
Also watch a youtube tutorial on gtx 770 installation and see what other people have done, helps out a lot :)