Peter is describing two different possible problems.
One possibility is carbon buildup in the prechambers. There is an MB special tool (glow plug reamer) for removing the carbon buildup. I don't remember exactly how much the tool costs, but seems like it was a hundred bucks or so.
The second possibility is that the glow plug relay is staying on after starting for some reason. It sort of sounds like this is what the guy gave up on. Like Peter said, this is probably not difficult to fix. Anybody with basic electronics skills and an understanding of how this circuit works should be able to troubleshoot it. He should be able to find a wiring diagram from Alldata. Your best bet is to seek out a mechanic who is familiar with the pre-1980 glow plug system. If I was going to just throw parts at it, I would probably start with the glow plug relay itself. Should be inexpensive at your local MB wrecking yard. Just be sure you get one from about 1977 to 1979. Later models would be different.
It's also possible that some previous owner has butchered the wiring in some way. If that is the case, it would be more understandable why the mechanic is having trouble figuring it out. I think this is unlikely, but a possibility worth mentioning.
2004 C240 Wagon 203.261 Baby Benz
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And remember folks, Only You Can Prevent Hilliary.