First off what your describing could be one of two things (i have fixed both).
#1. Air compressor clutch starts burning up about 90,000-100,000 miles or so. At first it does exactly what you described initially before stop working all together (or the clutch bolt snaps and the end of the compressor falls completely off). I replaced 3 of them on my 06 before shooting it of old age at 380,000 miles and each time the clutch was the problem. All I did was replace the compressor each time (no dryer, no orfice filter which is built inline anyway) and simply blow the lines clean, add some oil and pull vacuum and recharge. Each time I got around 100,000 mile before the next clutch failed (compressor never failed only the clutch).
#2. The blender door is pretty much an issue with all 06's. It can be repaired (as a home fix) through the glove box door and removing the fan (3 bolts). The broken blender door can be accessed from there. All I did was take some foil ac tape an cut a piece of cardboard the same shape as the old door and tape it to the fire wall side inside the fan box. That mode is the same as recirculating the cab (coldest). it does take a little longer to heat up when it's cold, but it will heat (for a lot less than the dealer will charge)