Check the heater valve. I believe that on your car it has the "monovalve". It is on the firewall near the battery. If it is square on top with four screws, you can take out those screws and raise out the guts of the valve. if the diaphragm is ruptured the valve will be flooded. Your MB dealer has a repair kit for about $35.

If there are no screws on top, your model has a different valve, and you will need to find information for troubleshooting the system. If this is the system type, it is likely that the problem will be the pushbutton control unit, but ensure it is your problem before buying one.

Good luck,