Have you changed your transfer case fluid at all? If not I would start there.
Drain it and refill w/ appropriate ATF and then take for a drive to get the new fluid where it all needs to be and then try to get it in and out of 4x4.
If this does not fix it then look up the service manual there is a sequence you can do to get the 4x4 system to blink codes through the 4x4 light.
I just had 4x4 issues firstly my 4x4 worked fine this season so far and then went to throw it in and had a buzzing from the trasnfercase control unit located under the dash/glovebox. Drained the fluid (I had changed it 2-3 yrs prior) and it was pretty dark and put new fluid in and it went right in and out of 4x4 w/ no blinking lights or disappearing indicator. Then sadly had a bad ABS/wheel speed sensor connector/wire that went bad and cause the 4x4 blinking and no engagement, fixed wire and fixed this problem.
In emergency situations I have read that you should be able to pull the ABS fuse and fool the TCCU to allow the 4x4 to engage.