I had some unpleasant transfer case issues last fall with my 04 1/2 ton. One of which was some faulty speed sensors. I did my diagnostics between the dealer and throwing some parts at it. Long boring story.
-Try disconnecting the batteries and resetting the system.
-Start the truck. If the lights come on at the switch, try shifting the case.
-If the lights blink, but no shift, its most likely the shift motor
-If no lights its most likely the dash switch. These were common failures on the later model trucks, but could have failed on yours too. The switch is the cheapest part (about $50) so if you start throwing parts at it, this would be the only one I'd replace without any further scan info.
-On occansion the transfer case control CPU has been known to be a problem, but not as much as the switch or the motor.
2012 Chevy 2500HD ECSB, 6.0L gas, auto, 4x4, LT
2003 F450, 7.3L PSD, 6 spd stick, 2wd, dump truck
1983 GMC K2500 pickup - working on a Cummins 5.9L swap
1987 GMC K3500 Dump, 6.2L diesel, TH400 auto - project plow truck