Back on Mar 9th I posted in this because of your comment of when I press the AC button the light will not turn on. I hope you saw it, but you just never replied. That light is turned on ONLY when the fan is in position one or higher,,. NOT in the lowest OFF position. The light is controlled right there in the HVAC module by the blower switch along with the AC switch . To turn it off, the lead from the fan switch off position to the logic portion of the HVAC module is grounded (-12 volts DC). The absence of the light on tells me that either the bulb is bad, you have the fan switch in the off position, the blower motor switch is bad (probably shorted) or that lead is grounded by the HVAC control module.
The lead leaves the blower switch on pin A of the HVAC module, and runs on a dark green wire that returns to the logic portion of the HVAC module on PIN 7 labeled on the schematic "OFF BLW MTR CONTROL". With that line grounded, the HVAC module is never going to tell the BCM to turn on the compressor.
So until you can get that light to turn on and off correctly, nothing else you check is going to work to fix your problem.
If you do end up replacing the module, be careful. I got one from an 06 to put in an 05 and they were different. I ended up robbing the switch out of the 06 module and putting it in the original 05 HVAC module.
Good Luck