From your description, the transfer case is stuck in 4WH.
The shifter if memory serves me, is what works your switches for the light and operating the lockers. SO even though the t case is in 4WH, moving the shifter will still work the indicator lamp and lock out for the lockers.
And most likely the jump is from running around in 4WH.
Sounds like the t case has a serious hurt.
And unless you have manual hubs, they never unlock. You have direct connection from the hub to the axle, to the diff, to the drive shaft, to the t case. The t case is what locks up to give you 4WD. The rest are all constantly connected.
Find another shop, as this one sounds like it doesn't know how 4WD works in a jeep.
97 Sahara, 74 Renegade, 72 CJ5, 55 Willy's (the Beast) Boss 302, 6:34 gearing, Bose 901 speakers.
God I miss that Jeep. Forgot the kinda Jeep, 80 SX4.