S600 W140 differential replace cost?
 

so week ago I bought a car of my dream, 98' S600.
168k mi, but in pretty good condition.
took it to the dealership for a free diagnose, they checked and said nothing urgent needs to be done, just some recommendations list of total ~$12k wow and yeah welcome to Mercedes world ;)

later same day, I pressed the gas to the bottom, wwrrrrRRROOOmmm! after 2 sec in the back under the trunk heard boomzz!-babah!-krsh-kr-krkr-kr-kr.....
and no connection between the transmission and the wheels, even when I put on "parking"
the kr-kr-kr-kr noise is heard even when just rolling

so obliviously there is no differential as is. but not 100% sure, I'm not a mechanic.
I got it towed to my place.

so my question is, how much it would cost to replace the differential, parts and labor?

thanks,
but turned out it's the left axle that broke down, and it costed me $840 to repair