Are you using a button to engage the CDL or relying on the transfer case being in 4Lo?
If the ignition is on, even without the engine running, when you either hit the button or if you haven't done the pin-7 mod, you should hear a click coming from a control box near the lower driver's door hinge. This relay box is what actually powers the CDL actuator.
The way I'm reading your post, you say you get no light AND that it won't engage. How have you tested that it won't engage?
If the parking brake is not engaged, transmission is left in Neutral, the transfer case in either 4Hi or 4Lo, and the CDL UNLOCKED, if you jack up a single tire you should be able to spin it. There will be resistance due to the viscous coupler, but the combination of the differential in whichever axle you are using and the center diff, plus the transmission being in neutral, should let the tire keep spinning (again, with resistance).
Same test with CDL engaged, there will be some play but that tire will stop dead.