If I recall correctly, our trucks use a sensor that does not require programing to the truck. It's possible that the receiver behind the wheel well (aka the Tire Pressure Monitoring Module) got damaged or disconnected though.
This video shows where it is:
The TPMS signals are received from the monitor modules by the "Radio Frequency Hub Module" that handles the TPMS, passive entry, keyless start (Push Button) and remote start (if equipped). It's on the back wall of the cab behind the seats. Hopefully that's not it though, replacing it is somewhat of a pain.
I also see that you have the 7" cluster, is that stock or did you happen to upgrade it around the same time? They changed the TPMS system used between 2013 and 2014, so if a later year cluster is installed the TPMS is the one item that will not work.
Bad or incompatible sensors I would think would just show no reading from the tires, not the service system error. When I had one replaced it took a few miles (< 5) before it started showing a reading.
-K