Not sure about MB's, but some vehicles I had in the past whould exhibit this "totally dead" symptom when (in that case due to damaged teeth on the flywheel) the solenoid would get stuck with the starter gear in the extended position. On those stick shift cars, the fix was pushing the car backwards about a foot while in gear (which turned the flywheel the right direction to "screw" the starter gear back into its retracted position). Don't think you'd have the same "stuck extended" problem, but if you've got juice at the battery itself, the solenoid might be the culprit in some other way.

Good luck. We California natives don't know from 20 below.