It wasn't until the next morning that I noticed my fan in front of the radiator had been running all night. The battery was just about dead, but when I turned my car back on the belt turned off.. Somehow the polarity got reversed. maybe. Anyone have any advice? I need to make a 2 hour drive today and might be in trouble if the fan isnt running.

 

first of all, lets make sure everyone is clear.

A honda civic does NOT have a belt-driven fan. It is electric, so no belt is running your fan

second, your fan should only turn on when the key is on AND the engine is warm enough to trigger the fan switch (called an ETC)

Now, as to why it turns ON when the key is OFF, and turns OFF when the key is ON.... thats very strange.

Have you had any work done to the car recently?

 

The relay is probably stuck. Open the underhood fuse box and pull out the radiator fan relay. That should stop the fan. Replace it with one of the other relays (such as the rear defroster, you won't need that until winter). If that restores normal operation buy a new relay.