This post is interesting:

Partial Electrical Failure

Have you checked all the fuses?

MORE QUESTIONS: Have you tried to start the car with the key while in neutral instead of park? Did you notice any other electrical irregularities like lights or accessories not working or any smell of melting plastic? Is the one click that you hear actually the starter solenoid or could it be some other relay under the hood that you are hearing?

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1993 400E, 256,000 miles (totaled)
1994 E420, 200,000+ miles
1995 E420, 201,000 miles