Issue with transfer case, hesitation while driving?

Yes, it will not move because it is all wheel drive, and the transfer case is trying to drive the front wheels but can't. Can you scan the car for codes please? I would use a CAN scanner. You can get a CAN scanner (Controller Area Network) which will work on most cars from Amazon.

Here is a video to show you how:

https://youtu.be/u-4syLc-ifQ

and

https://www.2carpros.com/articles/can-scan-controller-area-network-easy

Also, please go over this guide:

https://www.2carpros.com/articles/engine-hesitates

We need more information to help you, can you upload a short video of the problem so I can see what's going on? Please go over these guides and get back to us.

Good call, Let's change the fluids to see if that helps. Also, here is some information on the transfer case.

Sectional view of transfer case with code (430) Off road package

With code (430) Off road package
A permanent all-wheel drive with two lockable differentials (transfer case and rear axle) and an open differential (front axle) is used in the Off-road package equipment. The torque split of 50:50 % between the front axle and rear axle is specified as a fixed value in the transfer case.

The "Low/High" function in the transfer case can be used to select two gear ratios. The on-road ratio "High" is 1:1, the off-road gear ratio "Low" is 2.93:1.

The transfer case control unit (N15/7) and the rear axle differential lock control unit (N15/9) control the two ratios. Via the Low Range switch (N72s31) which is located in the lower control panel control unit (N72), the driver can switch over between the "High" on-road ratio and the "Low" off road ratio.

The differential locks in the transfer case and in the rear axle can be operated or adjusted by the driver via the differential lock selector wheel (N72s34).

The differential lock selector wheel is located in the lower control panel control unit.

The following control units are involved in controlling the transfer case and the rear axle:
Transfer case control unit
Rear axle differential lock control unit
Lower control panel control unit
ME-SFI [ME] control unit (with gasoline engine)
CDI control unit (with diesel engine)
ESP control unit
Fully integrated transmission control (VGS) control unit (Y3/8n4)

Further partial functions are described in separate documents:
Transfer case/rear axle differential lock control, function (with code (430) off road package)
Downhill Speed Regulation, function
off road transmission mode, function (except code (430) Off road package)
Transfer case oil supply, function
"Low/High" shift, function (with code (430) Off road package)
Interaxle differential lock, function (with code (430) Off road package)
Interwheel differential lock, function (with code (430) Off road package)

BB00.40-P-0256-11A Gear Oils (Sheet 235.11)

Agip. Rotra HY DB Synth
BP. Energear MBT
Castrol. Syntrans-AT

463 with transfer case 750.654

Esso Gear Oil. GP-D 80W
Mobilube. GX-A80W
Valvoline HP Gear oil. GL-4 80w
Mercedes Benz transmission oil sheet. 235.1

463 with transfer case 750.65 except 750.654

Please let us know what happens after the fluid change.

Yes, the adaptive learning can take many miles to relearn so I would just keep driving it. Let me know what happens please.