You're in luck, I just fixed one the other day doing the same thing. I am going to explain to you how the 4X4 system works and what can be done to fix it.
You have a trasnfer case that locks in 4wd and 4wd lo. Then you have a solenoid called an IWE(independent wheel end). It release vacuum to the hubs to allow the hubs to enge the axle on each side. There's a few things that happens. If you have the old style IWE solenoid,it will leak water into it and freeze and cause the 4X4 to do weird things. You must replace the solenoid to fix that. Then you have to inspect the vacuum lines going from the solenoid to the hubs. You may have a vacuum leak. Then if all of that is good, you may have a vaccum hub seal bad. If it gets to that point, you need to inspect the hub and the seal. The teeth on the hub get worn from the false engaging and will be worn.
I am going to look up the service bulletin and some manuals for you and will post them asap.
Thanks for asking!
Here is the service bulletin:
Some 2004-2006 F-150 and 2006 Mark LT 4X4 vehicles built before 4/24/2006 may exhibit a noise inXXXXXfrom the front Integrated Wheel Ends (IWE) and/or the 4X4 system being inoperative. The IWE solenoid may have ingested water and passed it to the IWE system causing water contamination in the vacuum portion of the system. A shorted IWE solenoid can set the codes C1979 and C1980. If either code is present, the 4WDH light will be inoperative.
Use the following Service Procedure to check and repair the 4X4 system.
I cannot find all of the pictures that I want. This may help. Here is a description of the slonoid operation:
Integrated Wheel End (IWE) System
The integrated wheel end (IWE) system consists of the:
The IWE system uses vacuum hubs that engage or disengage the front wheel hubs from the front halfshafts.
The IWE solenoid receives engine vacuum from the vacuum reservoir.
When the four wheel drive system is in 2H mode, 4X4 control module (PCM) supplies a ground path to the IWE solenoid to apply vacuum to the integrated wheel ends (disengaging the front hubs from the front halfshafts). In 4WD mode, the 4X4 control module (PCM) does not supply the ground path to the IWE solenoid, vacuum is not applied to the integrated wheel ends and an internal spring keeps the front hubs engaged to the front halfshafts.
Not special tools, of course air tools will help get some of thsoe parts apart. You have to pull the right front upper control arm loose and the outer tie rod end off of the control arm assembly and then you have to remove the front drive axle from the hub area. There is a small cap you have to pry off to access the nut on the end of the axle. The vacuum hub is bolted to the inside of the wheel hub. You will see a double vacuum line going to the hub and you will see three small bolts holding this hub in place.
Now, the solenoid is located right behind the battery mounted to the firewall. It's not hard at all to replace. You have to unplug the solenoid,remove the vacuum lines and unbolt it from the firewall.