Area of Concern:
Resolder these 16 pins - you really don't need to if it's just the A/C not working - but the other pins also had solder cracking.
If all else fails, resolder the switch. It's the 2x3(6 pins) closest to the black LED housing. If the LED does not turn on, try resoldering the 2 pins directly under the black LED housing
Test Your Switches:
If you have a multimeter handy, test the continuity of the pinouts. If the meter beeps steadily, your fine. If it's on and off, resolder the appropriate pins.
A/C pinout
Mode and Reciculation pinout
Rear Defroster pinout