So I put the 2003 Tahoe up on jack stands and noticed that with the '4-auto' button lit that the front driver tire and the back tires would rotate (but not the front passenger tire?). I tapped on the t-case encoder with a hammer and got it to shift to '2wd'. I heard the front differential motor unlock the front tires but it then went right back to '4-auto' on the button. At this point I suspect the t-case encoder motor so I removed it from the t-case and played with the dash buttons. The system intermittently would go into '2WD' and I could hear the front diff motor working but the encoder motor did not do anything. By the end of the trouble shooting the led's on the switch buttons were not lit at all. I suspect a bad connection inside the t-case encoder motor assembly and have ordered a new one. I believe the vibration and sound that was coming from the T-case area was due to going 70+ with the front tires engaged and the t-case was vibrating due to the computer trying to 'automatically' run the t-case with the t-case not responding to commands. Saturday the new encoder motor will arrive and I will install and (hopefully) any signal the computer is depending on from the t-case motor will be good again and it will shift normally out of 4-auto.
Save that old encoder motor. You can replace the range position sensor that's inside and probably have a good one for a spare.