There is no CE light? Probably not an O2 sensor, and I think the above statement is true, as the sensor is not in play during a rich cold-start.
I'm not familiar with the fuel delivery systems on the C230 (it's my own car, guess I better bone up) so I'm not sure if the car has a fuel pump relay (I suppose it does) and that would be a suspect.
Things to check:
Ignition: Plugs, plug wires.
Fuel: Pump, pump relay, filter.
There might be some stored codes even without a CE light, you might want to have them read.
The beating noise would have me suspecting the fuel pump.
1998 C230 "Black Betty"