I've solved my problem. Posting my solution here so that somebody else might find it who has the same problem...
To solve the problem, the EATC unit (the climate control head unit) needs to be reset. For whatever reason, disconnecting the battery does not accomplish this. The EATC needs to be unplugged from the wiring harness. This worked on my 2003 F150 Supercrew Lariat. Here are the instructions.
1. There are 2 vents in the center of the dash on either side of the radio. Turn both of these vents INWARD so they are facing the radio and towards each other.
2. Reach inside the vents and grab the inside edge (near the radio). Grab a firm hold inside of the vents, and pull the dashboard directly out. You have to pull fairly hard, but there is no damage to be done. There are merely 4 clips holding in this part of the dash. You are only disengaging these 4 clips. The center portion of the dash will pop right out around the radio and climate control unit.
3. Once the dash is removed, you will see 4 screws holding in the EATC unit. They are a 10mm head or Torx-20 bit. Remove the screws.
4. Once the screws are removed, the ETAC unit will pull straight out about 5-6 inches, just enough to access the rear panel.
5. The rear of the unit has 2 electrical connectors, and a connector with 5-6 vacuum lines attached. You do not need to do anything with the vacuum lines. You can easily disconnect both electrical harnesses.
6. Leave the unit disconnected from the wiring for a few minutes, then reassemble in the reverse order.
That's all there is to it. The entire thing is literally a 10 minute job and required nothing more than the socket or driver to remove the screws.
When I was done, the unit worked perfectly.