Hard to give a complete and thorough diagnosis over the internet without more information.
It seems that most people who have trouble with the shift motor don't get the indicator light to light up like you're getting. The indicator light is triggered at the shift motor. A couple of scenarios:
1) The shift motor is turning but, for whatever reason, the shift fork is broken or otherwise unable to perform the shift. From what I understand, the shift fork on these has plastic tips. While it seems rare, it isn't unheard of for the shift fork to go bad and not be able to shift.
2) The shift motor is not turning, but the indicator switches think it has turned. Others who are more familiar with the shift motor might be able to explain exactly how this occurs.
3) Some other electrical fault is causing the indicator lights to come on when told to go into 4H/4L.
I think at this point, the first couple of things I would do would be to get under there and see if the shift motor is doing anything, and then pull the shift motor off and see if I could manually shift the t-case (by rotating the shaft by hand). These two things should help to see if the problem is something mechanical in the t-case or something in the electronic shift mechanism.