The A/C compressor engages in the defrost setting and will blow ice cold ... Turn it to blow from defrost to regular a/c setting compressor does not engage. I have the basic 3 knob climate controls; no rear air.
I don't want to sound like an idiot, but do you have the back knob turned to the setting that allows the driver to control the setting in the back?
I've done that recently. I didn't realize that I had the driver locked out of the back area and when I turned the center knob to the correct setting, the air started to blow in the back.
Something as simple as that could be the issue. I hope it's something easy and not needed to be taken to the shop and costs money.