I have a 2006-2009 Dodge and the A/C compressor not turning on.

The A/C relay should not be soldered in for the Dodge 3500 2006-2009. It should be a removable relay located in the TIPM.
 
If an A/C compressor is not engaging, inspecting that relay would be a good start, however the rest of the A/C system would need to be inspected. Low pressure safety switch, A/C compressor switch, low refrigerant, are all trouble areas that would need to be inspected and replaced if necessary.