Another test you should do is make sure you haven't blown the in-line fuse close to the battery... Sounds like it is ok since things does run now from the battery. I would use a DC multimeter and measure across the two battery terminals to make sure which should read 12.6-7VC if the battery is fully charge. When you connect up to shore power it should read at least 13.6VC telling you the battery is being charged.
Most of my DC wiring in a 2-conductor cable so if that is what you have at the fan when you use a cutter to cut it lose it would cut across the positive and negative DC wires at the same time thus blowing a fuse somewhere or tripping a DC auto reset breaker...
It would be a good idea to make sure your battery is being charged ok when on shore power otherwise it keep draining down on you and won't be there to use when you need it... If it drains down below 12.0VDC and not get re-charged back up in a timely manner it may do internal damage to the battery and need replaced.
We enjoy the roof mounted fans especially when camping off the power grids where we can turn both the bath room and the bedroom ceiling fans ON and let them pull in fresh air through a couple of up front slightly raised window. Pulls cool air into the trailer at night... Actually having the vent fan in the bath area is pretty important for removing steam from the shower when being used. The steam from the shower could do some wall damage for you and needs to be pulled out of the room as soon as possible. My bath room fan comes when we turn the light on inside the bath room..
Just a couple of my thoughts
Roy Ken