2004 Silverado 4x4

I am having a service 4wheel light on the dash. Also I am having a problem with the ac on drivers side will not cool the same as the right side. Most of the time it works real good,its like the door is not moving I have looked at the door arms they seem to be working can these problems be connected? Maybe dash electronics?

I doubt the two are related.
As far as the 4wd could be one of 3 things:

1. Bad switch
2. Actuator
3. Actuator Module
4. Reflash the computer

As far as the 'service 4WD' light on the dash goes, you need a dealer with a tech2 scan tool or an equivalent to pull codes out of the transfer case control module. GM also had software issues with the transfer case controller and encoder sensor problems in that model year. Diagnosis of the code would be a sure way to find out.

GM also has problems with their heating and air conditioning mode door actuators. The position sensor inside the actuator will fail and send skewed readings about its actual position to the controller. The controller will see this and default the problem actuator (usually) to full hot. This concern will also set diagnostic codes if an actuator is having problems. This problem is also best diagnosed with a scan tool capable of accessing heating and air conditioning systems.