Squid04

Was it working before hand, or did you just put it into a system? (Did your computer suddenly stop working?)

Did you:
Reset CMOS
Install new gpu drivers (While using Display Driver Uninstaller?)

Before you pronounce it dead, DDU and reinstall drivers. If that doesn't work, reflash the VBIOS. If that doesn't work, it's probably dead

Try it in a different slot if you have more. Also, try it in a different system.

Okay, couple things:
 
I suggest you don't run anything intensive on that card right now. That GPU is not supposed to get that hot.  As for fixing it, I see 2 good options RMA the thing. Easiest solution, and it clearly has problems that aren't your fault You could try flashing the BIOS, i doubt the hardware died. It is POSSIBLE electrostatic shock or wear on the connector killed the DP, and it is possible the fan connector got disconnected or they got ESD damaged as well. but not likely. Not sure how that will affect your warranty, so the safest option it just to RMA. But if this doesn't affect warranty for you, you don't care, or the warranty period is over anyways, that is an option that may help. (also checking to ensure the fan cable is plugged in for the GPU fans isn't gonna hurt, either. if you're comfortable taking the card apart, then it's a free excuse to replace the stock thermal paste with better stuff anyways

Oookayy.. this should be fun
 
Is it working in 3D applications at all right now (over DVI), or no (just like, the desktop and chrome and stuff) Is it hot only under load, or even at idle? Do the fans never spin, or just not spinning because it's not under load? What does the fan RPM say in afterburner? have you tried setting a fan curve to make them always on and seen if that works?  
I would try to get as much info while using another GPU/integrated graphics first, then start using the GPU in question as needed to test it out. just in case. 

perhaps also try running a CUDA test while connected to integrated graphics, that'll help see if drivers installed properly and if the issue is strictly a display one

glad you got a solution

my pleasure. (feel free to choose a best answer, or leave informative reacts to posts that help you to show people your appreciation  )

I'mma look into it now 8) 

I've looked into it, and it has been acting as it should for now, thanks

Let me know if anything changes.

Uh no idea but 6C is crazy cold...are you playing outside with an open test bench?

6C, that aint right at all, considering right now with a 360 + 240mm rad on water I'm sat at 31C @ 4.6ghz

Yeah 6°C sounds very bad.
 
It's impossible to get temps below ambient unless you are using a wicked cooling solution
 
Check the temps again with GPU-Z.
If they are again 6°C or similar during idle, the card is broken and you need to RMA it.

Umm... little thing, the name of the graph is above the graph itself, not below.
Your GPU is 29°C, that's fine.