UPDATE:
I bought a new shift motor off of rock auto. I took it to my mechanic to swap out. He swapped them out and called me to tell me that the light was still on and the problem was not fixed. He said they tested the harness (plug) that plugs into the shift motor. There was power to the plug, but not coming out the end of the plug. So it seemed that the plug was bad. They could not find a new or used plug so they had to solder in new wiring. So far, and it has been about 30 days, everything is working as it should. I guess I wasted 200 dollars on a new shift motor. My vehicle is 2006 durango with 5.7 hemi.

 

Wishbone i own a 2004 dodge durango limited edition AWD 5.7 hemi .WE had the same issue .We back out of our driveway one day & it went on it own into low 4x4 and we tryed everything to get it out .I finally jack all 4 wheel off the ground & put 4 stands under it .I removed the transfer shift motor first u need to use a jack on transmission or the transfer case & remove the cross member thats holding your transfer case or transmission . There 2 or 3 bolts holding the shift motor . First take your neg off the battery . After u get transfer shift motor out & take the plug off the shift motor .You will need a #8 or #10 vise grips you will see the stub that i shift motor slid on .Put your vise grips on the spline stud make sure u sure the right vise grips that match the stub .You will need to get your transfer case back into AWD manually .make sure your dash switch is in AWD .U will need help you will be on the vice grip & have your helper start the motor & keep there foot on the brake & put the transmission in Drive & just want the tires to turn forward and let the brake up just enough to let the tires turn & then you need to turn that stub with vice grips make sure you do not strip or mess the gear stub up .You will feel the stub change in 4 hi then in AWD ,Then have your helper hit the brake put the transmission in park and shut the motor off . Now pretty sure your shift motor is bad .There not fixable .now the old shift motor has numbers & letters on the side .You will need to find one new with the same numbers & letters ok .I would get under it first and look at the shift motor and buy a new one it took me months to find a new one ok .I found a new one at . carparts.com they are real good i bought it and had it in less then a week .I think i paid like $150 .00 ok .JFI 2004 to 2007 new 2 nd generation are a nightmare in electronic issues .Remember the circuit board are all branded with your vin number and there no going out buying a used one and thinging it will work .You may get a used part like maybe a used computer but u will have to have it rebranded with your vin .And make sure the it matches your year & motor .Hope this help you out .I been in your shoes before .Also if your transfer case is going in & out AWD to Low 4x4 i would unplug it before the day u are driving 65 mph and it shifts in low 4x4 u will tear a lot of gears and drivelines up and $$$$ cost to fix my friend .