My CPU fans stopped working

The back fan uses Molex connector along with 7 other fans that came with the Azza Hurrican 2000 case. The thing is, the back fan connector is also connected to the two top/ceiling fans and they're working just fine, so I'm guessing the back fan is broken.
your guess is right on the money. The fans that were offered as suggested all use molex connections, with the exception of the PWM fans. Those are all for direct connections to the motherboard, not the case fan connections you have
If I were to get a new PWN fan, is it necessary for me to apply thermal paste to the heatsink?
if you just replace the FAN no, you will not need to do anything with the heatsink. the Noiseblocker fans I suggested are 3 and 4 pin compatible, as is the Cooler Master
 
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