I've had this problem too, thinking I had a BAD 4x4 CM, the one located in the glove box. I would DEFINITELY try the "BATTERY RESET" FIRST!! Clearly because I tried it and IT WORKED !! Here was my problem, obviously, no 4x4, on one of the worst snow days, tried engaging 4x4Hi to go up steep hill to my house. NO go. No nothing, no lights blinking, no clicking sounds, nothing. The next day, I tried troubleshooting the problem. I noticed when you first get turn the key, and all the dash lights come on, I had "4x4Lo" light up, but no "4x4Hi" dash light. Therefore, I thought I had a bad 4x4 CM. Was JUST ABOUT to order a new one from SilverState Ford in Nevada, when I decided to check here one more time for a CHEAPER solution. By the way, I also had problems with dead battery, which according to some, if you swap out battery incorrectly, it will "fry" your 4x4CM. That may or may not be true, but apparently if you do this battery reset procedure, it SHOULD bring your 4x4Hi back to life.
I did the battery reset. Just like others have posted. Remove the POS cable to your battery. Then, put key in ignition and turn. I did it BOTH ways, since I wasn't sure if you should just TURN and STOP just BEFORE you would "start" car, or if you should trun ALL THE WAY, as if you were going to start the car. Anyway, did it BOTH ways. Went back inside to warm up coffee and grab a piece of toast. Went back out after 5 mins, reconnected the POS cable to battery and then went to start car. BE ADVISED. At first, I didn't think it worked because the "4x4Hi" dash light didn't light up, just the "4x4Lo". However, when you actually go all the way and START the vehicle, I actually saw the "4x4Hi" dash light come one, and when I pushed the 4x4Hi button, I heard the clicking and voila, the "4x4Hi" dash light stayed on. So, I "guess" I have 4x4Hi now? LOL. We're supposed to get more snow in the next few days. Will let you know, but I'm pretty sure, from hearing the clicking both inside AND outside the vehicle, the 4x4 was engaging. Good Luck to all !