Vent runs continuously

The fan that blows air onto the windshield and onto the floor will not stop unless I disconnect the battery. It does not matter whether the car is running or shut off with the keys removed, the fan keeps running. If I turn on the air conditioner, it works properly, blowing cold air out of the vents on the dashboard. The AC seems to run independently from the fan that will not shut off. In other words, I can toggle the AC on and off, but the other fan continues blowing onto the windshield and floor. This happened for the first time yesterday. After riding home with the AC on, I parked the car, shut if off, then noticed the fan was still blowing air on the windshield and floor. I disconnected the battery, and the same thing was happening the next morning when I reconnected the battery. What could it be?