The Differentials are very rugged. It is the associated parts that usually fail due to age and high mileage
What's wrong with my Mercedes?
Driveline and rear end Problems
Sign of worn part when driving over rough ground
Knowing your rear suspension design and theory will help troubleshoot a problem
Nothing like having the right tool
Best way to test them is out of the car on the bench
Kent recommends just sending it out for professional repair