No offense to diesel cars or their owners intended...

My 1987 260E has had a problem starting for a long time - as in years. It has progressively gotten worse. It used to be just cold starts, but it is now every start. It is a beautiful car with the exception of this nasty problem.

I am so tired of passengers asking if my car is a diesel!

On starting, it first fires on just one or two cylinders, then a couple more, then all six. If it is not revved, it would simply shake and rattle for 10 or 15 seconds before it smoothed out. Once revved, it clears up, but occasionally gives up a faint puff of gray exhaust smoke. It's occasionally black, but that may reflect an annoyed HARD rev of the throttle tossing some carbon out.

I have heard that it could be all kinds of things. I remember a similar problem in a 1980 VW Rabbit I had in college. I changed the fuel line check valve in that car and that solved it.

I therefore tried changing one of the two fuel line check valves in the Benz, but perhaps I guessed the wrong one, (I had a 50/50 shot) or this wasn't the problem. No change.

I checked the plugs, rotor and cap. All good. I must guess that is most certainly a fuel injection problem, not an ignition issue.

What tests can/should I perform?

Appreciate all thoughts and/or uneducated guesses.