2004 suburban rear air not working

Yes there is.

https://www.google.com/search?q=2004+chevy+suburban+rear+ac+blend+door

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There is a blower motor control processor for the back blower - it takes input from the front control and the rear control and decides the fan speed. That processor could be faulty, or the blower motor, or a 30amp fuse in the engine compartment.
In the front system you have a controller and blend doors that direct air thru the heater core and evaporator. You would need to check the operation of those blend doors.

check for power and ground to rear blower motor. if no power check for blown fuse. if no ground check for bad blower motor resistor for rear unit.

The dealer is probably right, but before you lay out that kind of money, locate the actuator and check that it has not become detached or that the arm on the flapper that it activates has not broken off. If you can remove the actuator put 12 volts across it from your battery and check if it works. You may find a wiring problem which could save you a lot of cash. You should also be able to get an actuator from a breakers yard for a lot less than the dealer's price.

Sounds like there is a issue with the front blower motor I would check your fuses first because sometimes the motor jumps in voltage causing the fuse to blow. Check your user manual for location also if that is not it and the motor is getting power it could also be the switch that controls the blower motor.

If rear a/c blower motor working but just not cold, it's going to be a clog expansion valve for the back unit, if not blowing air bad blower motor.

Check and replace the right side temp-controller.

check the AC relay...not the fuse but the relay

There is probably a temperature blend door in the duct-work under the dash that is inoperable or stuck in the heat mode.

the bvery first thing that i would check would be the fuse. from there i would check and make sure that the blower motor relay for back there is operative. From there it could be a wiring problem to a bad motor