As others have indicated, it sounds like you are getting some terms muddled up.
The processor fan will be inside the computer attached to the largest heat sink in there on the main processor chip.
The fan you can see when looking at the back of the machine from the out side is the power supply fan.
You may also have any number of other fans scattered around the general casing of the computer, these are simply called case fans.
As a general rule, all these fans should be running at all times, there are a few rare exceptions to this when certain machines can and will shut the processor fan down completely if the computer is not doing much (this is very much the exception and not the rule though!)
If the fan you can see from the rear of the computer is not working then you really need a new power supply (it's possible to replace the fans, but they are not generally considered to be a user replaceable part)