W202 fuel pump as the cause?

[BenzOnline]

I have a 99 C230K with 55,000 miles. Recently it developed a hard to start cold start.....shakes and stalls at the first start attempt and then catches but hesitates for about 5-10secs at the 2nd attempt. Then its all good for the rest of the day until it sits for 8hrs or so and you turn it on again, such as the morning.

I was told the fuel pump makes the pressure and it likely the cause. I was thinking based on older MBs and how they run, that it would be some type of cold start valve or the like.

Anybody have an opinion? Please help!