I don't have knowledge of that specific car but I can tell you my experience with some non-Mercedes cars that had the same symptom. Most fuel injected cars have a safety circuit to cut off the fuel pump if you get in a crash. In my personal experience this was the problem. The start circuit overrides it so you get the symptom you describe. With the old mechanical air flow sensors it was a contact that would wear out. I am not sure what Mercedes used on that one. Hopefully one of the gurus will now tell you what specifically is wrong. Have you searched?

Mike

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra