The fan beeing out wouldnt be the cause. But to fix it, just splic the wires together and add solder to hold it, insulate with electrical tape.
I would gather that the solder on the other pins may be causing you the trouble. Check to make sure they are not shorted, use a multimeter if you can get one, they are cheap at radioshack for crappy ones, but thats all you need for basicaly a short no short purpose. You can use desoldering braid to easily suck up any excess solder.
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