People getting rid of cars for simple problems seems to be becoming a common trend. Let's not jump to hasty decisions here!

If your alternator had issues, your battery would die as you ran the vehicle - faster with more load like lights and radio.

You are having the car just suddenly die. As you said, you waited 10 seconds and cranked the car back up. If your alternator were bad and the battery had died, this is impossible. Not just on a Mercedes, but on ANY car.

You have a main battery connection that is broken, loose, or corroded somewhere to the point that it is losing connection. My hunch is on the negative strap from the body to the battery since you have everything in the vehicle dying out.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]