Diagnosing 4WD problem in GMC Jimmy

[Gsmith2030]

Have a 2000 GMC JIMMY and the 4WD doesn't work. Here's what I know:

All electronics are working. Normal lights/button behavior on dash - blinking for a few seconds then solid on whatever button was pressed. Vacuum system is working, collapsing the diaphragm under the battery. Cable to front axle is being pulled by diaphragm and moving freely. Split shaft was removed/checked and all gears look excellent. 4LO engages the rear axle when selected. Checked Transfer Case fluids - blue and clean, and at proper level.

 

All I can think of left is the front differential spider gears. In 4WD, I can freely turn a jacked-up front right wheel. Can anyone advise a diagnostic procedure to determine if the problem is the differential, or to verify how (by oneself) one can tell if the transfer case is engaging the front driveshaft?

 

Thank you!