Removed the bracket holding the fan motor, replaced motor with new motor I bought. It would have taken me less time, but the fan blades were hitting the bracket when I spun it after installation, so I took the whole thing apart again to make sure I didn't screw something up. I hadn't, so I ended up just bending the fan blades until they spun freely.
I did have to replace the wiring clip, but it wasn't a big deal at all and everything I needed was included with the motor.