The xDrive motor appears to be in very serviceable to me. The main Worm gear set is in good order as is the planetary set. The lubrication looks a bit dry so it would be worthwhile to wash all parts well and renew the grease. Use a good quality, high temp gear grease.
Just to clarify, this is an ATC300 Hetzel transfer case ...
http://www.fzth.de/en/catalog/parts-catalog.html. Take a look at the "TO THE TRANSFERCASES PARTS" link on that page.
I don't know if you or the shop drained and checked the oil but that would certainly assist in a proper troubleshooting. If the oil is clean, doesn't smell burnt and is filings free, then I would highly doubt that the T-Case is the problem. At that point you may wish to move up the powertrain.
Keep us posted with what you find.