There doesn't seem to be a lot of resolutions to the problem I had on my 2000 Bravada with a NV 136 transfer case so I thought I would post what I found on mine.
I have been chasing a problem with my AWD where it doesn't go into AWD but I also don't have a service light on either. Here is what I found, I started by changing the transfer case shift motor with one I had from a Chevy Astro. That didn't cure my AWD problem but it did cure my transfer case binding problem, Apparently it was keeping the transfer case engaged enough to give me the shutter, next I read several posts about bad tccm modules so I swapped that with no Improvement. Finally I shelled out the money for alldata and got wiring diagrams, what I found was it is a fairly simple system that only compares the front drive shaft speed to the rear and locks in the front if the rear is spinning faster, so I put an o-scope on the rear speed signal wires and I had 5v going out but nothing coming back. I thought SWEET bad rear shaft speed sensor so I swapped the sensor out of the parts astro. STILL no AWD!!!!????!!!! upon further examination i found the pin on the tccm connector for the rear drive shaft speed sensor was rusty and not making a good connection with the wire. I Mickey moused it just to test and yes i had AWD!!!!! so today I ordered a new connector with pins and will be installing them when I get them in.
I hope this helps people that have no service AWD light and no AWD. Make sure you check the connector on the TCCM with a flashlight it was tough to see the problem.