Not having the ESOF tranfer case, I have never had to work on these units BUT here is what the manual says to look at with your symptoms:
4WD mode switch.
Neutral safety switch.
Brake pedal position (BPP) switch.
GEM.
Transfer case.
Digital transmission range (TR) sensor.
Circuitry
I'd start by checking the relays and maybe get someone to engage the 4hi to 4low switch while you listen at the tranfer case to see if you can hear/feel if the shift motor is operating.
4WD mode switch.
Neutral safety switch.
Brake pedal position (BPP) switch.
GEM.
Transfer case.
Digital transmission range (TR) sensor.
Circuitry
I'd start by checking the relays and maybe get someone to engage the 4hi to 4low switch while you listen at the tranfer case to see if you can hear/feel if the shift motor is operating.