My '91 560SEL W126 has an annoying starting issue. On turning the key to start, it will fire immediately then die. If I keep the key turned or if I turn it off and start a second time it will catch and run, but the engine and the whole car shakes for about 3-5 seconds before it smooths out and runs normally. It is worst from a cold start and is hardly noticeable on a restart after the engine has been running for a while.

I have replaced all the spark plugs, distributor cap and rotor with OEM spec parts (Bosch) and the leads are fairly new. Other than the initial start the engine runs very smoothly and seems to be producing normal power.
Any ideas?

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1991 M-B 560SEL Arctic White/Grey 99,000 Miles
1987 M-B 300SDL Ivory/Palomino 229,000 Miles (sold but never forgotten)
2006 Volvo XC70 Blue/Beige
1999 Porsche Boxster Arena Red/Savanna Beige
1986 Porsche 928S Goldweiss/Brown