Does the blower motor run okay when the key is turned to the first position, before starting the engine? Sometimes in my '87 190E after starting the engine my blower would stop. The problem became more frequent. Then I discovered if I back off the key rotation a touch counterclockwise, the blower would run again. There must be something delicate in there about the switched electrical circuit, like it's meant to cut the blower fan off while the starter is cranking. I hope you are lucky and find a simple solution like that.

I had a much bigger problem develop when my heater core recently split and dumped hot antifreeze all over my feet. I clamped off the hoses under the hood and have been running without heat for a couple months while I get up the nerve to disassemble the dashboard. Even northern California is getting colder and colder. I found an encouraging technical article here that looks like it was written just for me. We'll see how it goes...