The condition you describe should never happen. It sounds like a bad alternator. If it's the usual MB prices thats probably three hundred plus. You might check the battery voltage with the engine at a fast idle, it should be about 13.5 volts.
If it's much higher, I'd be real careful about turning on the radio etc. The last thing you want to do is fry all that expensive Bosch electronics.
The well informed tech experts that frequent here can give a better diagnosis, but that's my two cents worth.