If you aren't getting the light in 4Hi, then the solenoid in the front part of the transfercase is not engaging. This is not the transfercase motor, as it only moves when you go into 4LO. Sometimes the solenoid will get stuck. If you take a rubber head mallet and bang on the front of the transfercase while the switch is in 4HI, it may engage. I have done this on my Explorer, when I still had the stock transfercase in it. If that doesn't do it, then you will need to have the codes read. If you have an OBDII, then you can read these yourself, or go to the dealer and have them read it.
There are 2 electrical connectors going to the transfercase. One goes to the transfercase shift motor. Its a pretty big connector, towards to back of the transfercase. The other one goes to the transfercase solenoid, which is towards the front of the transfercase. It has only 2 or 3 wires IFRC ans is sitting on top. Check to see if those 2 connectors are infact connected. Usually if the shift motor connector is not connected, it will make your 4wd lights blink, so if might be connected but not properly or enough to make a good contact. Hope this helps. Please keep us informed