Battery is brand new. I can get the engine started but only by cranking it for a long time. Not enough to hurt the starter, but WAY longer than it should.

I'm on my second relay. The second one came from the yard where I got the engine. Using the original relay I can pull the guts and force the relay that makes the six poll switch closed and the engine will start right up after holding it in by hand for 20 seconds, even stone cold.

You're confirming what I suspected, that the relay is bad.

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1988 300SE 83K+
1991 350SDL 283K+