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I believe this is the same truck with a different post too. Regardless, we need to start at the beginning by making sure power is available to the actuator. Take a look at the picture (wiring schematic) and confirm that fuses 34 and 111 are good and are providing power to the relays. If they are good, locate the relays under the hood in the relay box and remove and inspect the connectors. Here is a link that shows how to check a relay:
I am basing this diagnosis on the idea that the transfer case actuator is not working. You mentioned you did not hear an activity there.
If the fuses are the relays are good, take a look at picture 2. It is the wiring schematic of the 4wd system. Please note that this vehicle has a 4wd control module located under the dash, behind the glove box. What I am going to suggest will either indicate the module is bad (which will need tested by a shop) or the actuator is bad.
Simply disconnect the connector on the transfer case. Check pins 1 and 2 for power while you have a helper change the mode of operation indicated on the picture. Note: Based on when the vehicle was produced, picture 3 may not be valid.
If you do get power, then I suspect the motor is bad. If there is no power, the module will need tested with the proper test equipment.
Let me know if you have other questions.
Images (Click to make bigger)
Saturday, November 3rd, 2018 AT 6:03 PM