Blower motor doesn't work when turned on but works when hot wired to the battery?

Short Answer, I would replace the BLOWER MOTOR RESISTOR after checking the fuse. This should take care of it. In extreme cases you may have a bad wire and may need to trace the issue down. Hopefully a squirrel or something didn't get in there and cause damage.

Blower Motor Resistor Location

Troubleshooting the Blower Motor

Easy test; apply battery positive and negative directly to the blower motor. If it works, great. Not the motor.

If the blower motor only works on high speed; not the motor. Replace the Blower Motor Resistor.

If the blower motor doesn't work on any speed, you can test the motor first and determine if you need to replace the motor and or the resistor.