Fan stopped working on 560 TI, how to install new cooler?

Hey everyone. The other day I was blowing the dust out of my computer case because I was going to instal my new 3570k and z77 mobo. I may have made a mistake using the blowing function on my vacuum meant for cleaning a car instead of canned air. Once I got everything installed, I noticed one of the two fans on my card was not working. Even worse, it's not that it simply did not spin, but when I tried to spin it manually there was resistance. Even with the computer off, the other fan would spin easily if I gave it a nudge, not the other. So I obviously messed up the one fan with the vacuum. So here is my question

I can still play games and everything fine, since one fan is still working and my case (antec 1200) has oodles of airflow, but I want to replace/upgrade the cooler that comes on the 560 ti. Not saying that stock cooler from MSI was bad, but I kind of need a new one now that one fan is dead. So, what cooler would you suggest that is in the 50 dollar price range, and second...how do I do take off the old cooler and install the new one? I have built my last 2 computers, but have not messed with the cooling on my gpus before. Thanks for your answers!