Alright, it's time for a test if your up to it.
Have someone you trust help you here. Explain to your helper the procedure you just told us (yes, you did it correctly) and let them handle that part. Meanwhile, you climb under the rig and place your hand on the shift motor on the T-case, and get close to it so you can hear whats going on. Now, you have to mind the helper and the exhaust so you don't get harmed doing this.
After the engine is running and it is placed in Neutral, with foot on brake firmly,
Then climb under and ask the helper to shift from high to low range when your ready.
When it is switched from high to low, and back to high, you should either hear or feel or both the shift motor engaging. This is a simple test to check it.
Okay, after thats done, 1 of 2 things are going to happen here.
1) You find the shift motor working.
This eliminates the shifter and brings up other problems. (will get into that more later if needed)
2) The shift motor did not operate as supposed to. Kill the engine.
This does not mean its bad necessarily. The next thing to do is unbolt it but leave the harness plugged in. Start the engine, Repeat the test again with your helper and see if it works loose in your hand. Kill the engine.
If it does work loose, there might be a problem with the t-case, or the shift motor is weak.
Next test....With shift motor off ( ziptie it to the frame with it still plugged into the wire harness for now). Use a pair of simple pliers to move the shift rail that you see coming out of the t-case that the shift motor covered. Notice the markings. You will see H-N-L. That triangle looking nub points to what position it is in. It does not turn in a full circle, this is important, it will only turn to the H & L position and not beyond. Start the engine, place it in Neutral. Have your helper gently rock the rig front to back, as you turn the shift rail to ease any pressure off the drive train. Turn it from H to L, but don't force it past. It will click when its in gear, and stay.
Okay...did it shift?
Yes...Great! Tcase is most likely good.
No....Bad news. T-case is most likely broken. This can be a cheap fix or an expensive fix. No telling until the case is split.
Hopefully you don't have to go thru everything here, but just in case, I went ahead and told ya so in case I don't get back to you for awhile, you have something to mess with.