I had this problem as well and must say very little about this on the internet available whilst it seems to be a common issue!! The re-circulation button is to cut air "fresh air" (air from outside the cabin) off from entering the intake gate and car's cabin. HINT - If you push the re-circulation button whilst the Air con is running you will hear an increase of the volume of air moving through the system (this is natural) and gives you a clear indication the re-circulation door/gate is working. If this is not happening it could mean a few things- 1. electrical problem, 2. re-circulation valve not working 3. Gate opening mechanism not working but most common - 4. The vacuum pipe under your battery has perished due to the acid from the battery. I fixed the vacuum pipe and Re-circulation gate is working again fine, cheap solution! So in feature I will start with inspecting the vacuum pipe first as you only have to remove the battery and battery holder and not the whole dash!! if not that .... then big work!

The Chrysler manual is not very good on this with NO explanations of the workings of the intake gate! also removing dash not well described but nice to use as guideline.

Good Luck hope it helped.