Sapphire HD5770 1gb fan issues?

Hi, I've been having issues with my HD5770 for a while now and I'm looking for some help.

For the longest time, my graphics card worked perfectly with my computer and everything was fine, I never had cooling issues or anything like that and there really were no problems. Recently my computer would power up for a little while, seem to be working alright, but then shut off if you tried to use it for an extended period of time. Consecutive uses would make the computer shut off earlier than it had the try before, so I assumed the card was overheating. When I opened the case to have a look, I noticed that the D4000 red led was lit and googled for similar issues to my own, and it turned out that the led was related to overheating issues.

When I looked inside the case I noticed that while the fan was turning, it was bugging along slowly and not spinning correctly. I decided to take the card out, apply new thermal compound (along with my CPU) and then put the components back in. Since using the thermal compound (and compressed air to clean the fans and heatsinks), the CPU purrs is a lot cooler, but the GPU does not work at all.

Now when my GPU is put back in the machine, the fan does not turn at all. All 3 green leds on the card light up and it seems to run fine for a little while, as it had before, but it eventually shuts off (as there is no fan movement) and again, consecutive uses shorten the amount of time the GPU works. I've taken the GPU out again, but I'm clueless about what to do next, should I buy a new fan? There is no debris in the fan and when I spin it lightly with my finger it seems to spin perfectly? Although there is no resist from the fan at all, it is completely loose. I don't know if that is a bad sign.

The GPU is just over warranty by a few months. I also have no idea where to buy a new fan if that's what I need.

Thanks for reading!