If its the same controller as in the 1st gen w126, then it takes variable voltages to control fan speed. You can put 12 volts to pin 12 on the controller to see of the fan runs. The fact that it runs at all tells us as the fan is at least semi functional and that the controller is able to send it high voltage at least( judging from the fact that it works with the key in run position.)

Once the car is started, try backing off the key just a touch to see if your switch is worn. Just turn the key counter clockwise without turning the car off to see if it makes contact.

The age of the brushes and fan motor will delay it starting on low speed and then not start at all on low speeds. Then it will not start unless you tap it while on defrost mode.

It sounds like a contact issue to me from the fact that it shuts off directly after startup of the engine.

Another issue that you could be going through is low voltage across the system. You may want to simply check the voltage at the battery or cigar lighter while the engine is running to rule out the charging system as a culprit

You also have a Klima relay which most likely could use a wire brush at the contacts. That relay is located in the engine compartment near the fuse box on most mercs.

The walk through of how to troubleshoot the fan motor is posted by Brian Carlton. If you search "Brian Carlton that's what we are here for" you'll get his excellent walk through.


Thayer

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77' 300D, "Cartman" SOLD @ 150K (didn't know what I had)
83' 300SD, "The Superdon" 325k+ @ 28mpg
95 E320 wagon, "Millennium Falcon" 231k+ @ 24 Mpg
95 E300D, "Sherley" 308k @ 33.69 Mpg, currently anticipating a head
99 Suzuki Intruder "Trudy" @ 45 mpg