I have had these same symptoms with my '98 E320 for the last FIVE YEARS. It happens every 20-50 times my wife tries to start the car, but it has never proven to be a real problem, after several tries the car does start. The symptom is always the same: turn the key and you get one click (sounds to me like the solenoid) but no crank. After another 1-3 tries the car will star as normal. Go figure.

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64 230sl, my daily driver
94 E500, sold
98 E320, family and dog hauler
04 C240, safe machine for teen drivers, but a poc
08 audi a4, yes we have gone to the dark side