Transfer case is not working

The light flashing is telling you that the shift motor has not engaged 4HI. The GEM senses that this has occurred and when it doesn't the light flashes. This means either the shift motor has failed and can no longer make the shift. Or the wiring is the issue and the motor doesn't get the voltage necessary to make the shift. Make sure you check the wiring and the ground. It is very common for the ground to become brittle and brake and this will cause the light to flash like you are seeing.

Due to what you have replaced already I am sure you have a wiring issue most likely at the shift motor connector on the back of the transfer case because this is open to the elements which is bad for wiring over time.