Whoa!! Sounds to me like your diff. is doing what it is supposed to. Before you start tearing stuff apart, consider the following: A limited-slip or positive traction (yes they are the same thing) differential does not mean that when one wheel loses traction, the other wheel takes over. When one wheel loses traction, the other continues to move forward only under the torque required to overpower its internal clutches (if that's the type in an MB), not at regular speed. Were you not still moving forward even though one tire had no traction? Furthermore, if MB uses a Torsen type differential, they can lose traction altogether as the traction wheel gets a certain ratio (called the bias ratio) of the spinning wheels' torque. If the spinning wheel loses all traction, your sol because the torque=0 and anything times 0 = 0.
Check out this thread...