Sounds like a turbo issue to me too. Does the 350SDL have the overly complicated vacuum wastegate setup, or is it pressure operated like the 300SDL? It won't set any speed or acceleration records, but it should get around pretty good in town. The black smoke is a very good indication that there's a lack of air. Has the manifold ever been off and the coke/sludge cleaned out? If it hasn't, you could be in for a real shock. My SDL's was choked off to the point that the intake runners were only around 2CM in diameter because of the coke/sludge buildup.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]