Edit: Repairman is here. Hurray.
Edit2: Apparently it's a bad motor. They're going to "build a new one" and come back with it. The second guy said that it was from the old people who owned this place and they throught they had changed them all out, but I guess they missed a few.
Edit3: 1 new motor, 1 new wire box (apparently the wire box was telling the motor to turn on even though it was burnt out), and 1 new filter later and my house is much cooler. I believe the cats are much happier for it.