I have pretty much the same issue on my 87 300D. My money is on my battery being just plain old. It is 10+ years old and is due to be replaced. For some silly reason I just can't seem to make myself get it done. Maybe it is the MB 3 point star on the battery. I just don't know. For now I'm keeping 100ft of 12 gauge extension cord and my 2/10-30/60 amp start assist/battery charger in my trunk.

I know, just replace it.

-Jim

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1995 S350D, Green with black leather interior.
Bought January 2008 w/ 233,xxx miles.
I did 22,000 miles during the first year of ownership.