hi
I have a 85 500sel that was acting up witrh problems like you stated.I was convinced that i had a pump,injector problem,until after reading thru the posts on hard starting. quits when running,no fuel , etc I noticed a common thread was check the fuel relay,(use the search button) in there I found a way to open the relay and check it,Mine was broken,I ordered a new one from fastlane (click on buyparts at top of page)for about 60 bucks ,installed it and a whole bunch of problems just went away like magic. My thanks to the guys who posted and phil at fastlane,
Cliff