I bought a 2003 Yukon XL and had the same problem. From what I've read it's a common problem, and the failure is the mode and temperature actuators for the rear rather than the HVAC system itself. On mine, the actuators are located above the passenger-rear wheelwell (on the inside of course).
I would take off the inside panel there and then look at the actuators (there will be 2...one for mode, one for temp). See if they move when you turn your knobs, and then go from there. If they don't move, it's them or the control board (should be located there with the actuators) that is the problem. Start there.
