I just had the same issue with my 99 e300. All the warning lights were good. It sounded like it wanted to start, but stumbled. I was advised by MB to floor it, and then hold the key on for extended time, like 30-45 sec. After 10 or 15 attempts, it started hard and rough, then smoothed out. Turned it off, then started it again, worked fine.

The next day, after sitting all night, I had the same issues. At the advice of fellow posters here, I looked at the clear fuel lines around the fuel pump, filter, fuel shut off valve and found several of these lines had no fuel in them. It showed no indication of a fuel leak.

I had it towed in, (because I am still under starmark).

MB found the fuel shutoff valve was leaking air into the system. They replaced it, all is well now.

The air leaking into the system allowed the fuel to drain down into the tank. Essentially I had to prime the fuel system each morning, in order to get it started.

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1999 E300 DT 178k
1960 Ford Thunderbird Convertible 82k
2000 BMW R1200 CE 12k
2000 Nissan Xterra SE 145k
1994 Go Ped 1,000,000 miles