Rebuild that thing. Its easy. I was in the same boat as you, push the button... drive in circles, figure eights, ect... and nothing. Not even a sound when pushing the button.
Took an afternoon and rebuilt it and she works great. (would have been 2-3 hours but I snapped one of the small bolts that holds the cover on and had to drill it out). There were two issues with mine. First was I found a piece of metal in the "gear" that comes directly out of the electric motor... dont know if it was there or not before. Second problem I had was that all the grease on the inside had dried up into powder.
Take your time and be care not to snap the two little bolts that hold the backing plate onto the housing and not to damage the plate as you pry it off.
Get some good grease to rebuild it with, and a nice gasket maker to seal it back up with because your probably going to wreck the gasket.
Its pretty easy to do. As for checking the functionality of it. Pull the locker off the axle and plug it bag in and then have a buddy push the button with the power on (engine need not be on if I remember correctly) if it works the gear will spin... and you probably have something up with the plate gear in the axle or somthign is misallingned. If there is no movement or noise then you may have a electrical issue.
Mine made no noticible noise when attached to the axle, but when it was off the axle you could see it was trying to engage but could not spin the gear.
We did not pay attention to how we pulled everything apart so we put it all back together and locked and unlocked it a few times and the actuator seemed to "recalibrate" its self.
Then as others said, jack up the driver side rear and spin the wheel to make sure its unlocked... then use a flat head screw driver to manually slide the plate gear into the locked position, then check that the wheels is locked.
make sure the axle is in the locked position as well as the actuator and put it all back together.
All the links and instructions should help.
This is the walk through I used. Check out the pictures too they help. I was expecting my locker to look like his since my rear axle is super rusty... but mine was in pretty good shape.