The way to determine what is wrong is not too hard, provided you are physically flexible!
If the fan motor is running with the key "OFF", then get into the cavity where the motor/resistor is and measure the voltage on the center pin of the three pin connector on the end of the wiring that goes to the resistor. DO THIS WITH THE CONNECTOR UNPLUGGED from the resistor.
If you have voltage on that center pin when it is unplugged from the 'resistor', the climate module is at fault.
The "map" of what voltage you should see at that pin looks like this: