Do they all go back off or does one stay on to indicate what gear it is in?
when you try to shift to 4WH or 4WLow does the button light blink for a while and then go out or fail to blink or try to shift?
And does the 2W light stay on and remain in 2W with 2W light on or off?
Can you hear the transfer case motor try to shift?
Have you checked all wiring and wiring plugins on it?
You can pull transfer case codes by grounding pin 13 on the diagnostic connector and turning key on.
Then count the shift light button blinks.
Post back codes or blinks.