If I have voltage going to the blower motor from the resister on a 2008 trailblazer with auto climate, why would the blower motor not work

This vehicle doesn't have a blower motor resistor ! It has a blower motor control module , if you have automatic climate control !
If manual climate control , then there is a blower motor resistor assembly !
Blower Motor Control Processor The blower motor control processor controls the speed of the blower motor by increasing or decreasing the voltage drop on the ground side of the blower motor. The HVAC control module provides a low side pulse width modulated signal to the blower motor control processor over the blower motor speed control circuit. As the requested blower speed increases, the HVAC control module increases the amount of time that the speed signal is modulated to ground. As the requested blower speed decreases, the HVAC control module decreases the amount of time that the signal is modulated to ground.
Air Speed - Front Control
The blower motor forces outside air into the vehicle's interior. The vehicle operator determines the blower motor's speed when the driver places the blower switch in one of 5 blower speeds. The blower motor will always operate in any switch position other than OFF, as long as the ignition switch is in the RUN position. The blower motor and mode switches are located within the HVAC control module. The blower motor OFF input is connected in series with the HVAC control module by the off blower motor control circuit.
Depending upon the selected speed, power is provided to the blower motor from either the ignition 3 voltage or battery positive voltage circuits from the fuse block. The battery positive voltage circuit only provides power when the High blower switch position is selected. Power and ground are provided to the HVAC control module by the ignition 3 voltage and the ground circuits.
Low Blower Speed When the Low 1 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the low blower motor control circuit. Voltage is divided between 4 series resistors, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
Medium Blower Speeds When the Medium 1 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the medium 1 blower motor control circuit. Voltage is divided between 3 series resistors, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
When the Medium 2 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the medium 2 blower motor control circuit. Voltage is divided between 2 series resistors, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
When the Medium 3 blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the medium 3 blower motor control circuit. Voltage is divided between a series resistor, a blower relay, and the blower motor to achieve the desired blower speed. The blower motor is grounded through the ground circuit.
High Blower Speed When the High blower speed is selected, the HVAC control module applies voltage to the blower motor resistor assembly through the high blower motor control circuit. The voltage energizes the blower relay, causing the blower motor to be connected directly to the battery positive voltage circuit. The blower motor and blower motor relay are grounded through the ground circuit.
Go on you tube an check out videos on trouble shooting blower motor circuit
Chevy Trailblazer EXT Blower Motor Won Turn Off