I recently fixed this on my 06 Escalade. First I took the rear access panel off and watched the actuator as a changed the temperature using the controls. As expected, the actuator wasn't moving at all when I changed the temp.
I ordered a new control module, and a new actuator and installed them both. I watched again while changing the temp and noticed that the actuator was now moving as I'd expect it too, but the air coming from the vents still wasn't changing temperature (I had HOT only).
I took the actuator out again, and touched the plastic rod that it rotates; that plastic rod is actually part of the blend door itself, and when I touched it I realized it was just 'free wheeling', it had broken away from the blend door itself.
I went to my local scrapyard, found a Yukon with rear HVAC and tore apart the HVAC box, taking note of how it all comes apart. I removed the blend door from the donor Yukon and took it home. Then I careful repeated the tear down procedure on my Escalade's rear box, installed the new blend door, and put everything back together.
It's actually a fairly easy job, but you need to go slow and take your time. There are lots of little clips to break/lose if you're not careful. You also need to be careful when moving/handling the rear heater core and lines, you don't want to mess those up.