Shouldn't use TIM twice, What is loose? the fan or the heatsink? You may not need to pull the sink at all but if you do, while you have the fan off you may be able to find out exactly what is loose. Possibly placing a shim under the fan clip, one of the two that hold the fan to the heatsink will help. if the entire assembly is loose you should be able to fix the pushpin w/o removing the heatsink at all. Check your pushpins first.
You don't need to replace your vid card for a fan, you can replace the fan.
Also, next time you trouble shoot fans in your case please post one thread, it would be much easier to follow.