James L.,

If your measurements showed the Voltage across the battery was lower with the engine running, you either have a short in one of the accessories you had running or you have a defective alternator, or both. You may have damaged the battery as well.

I think you should have the alternator checked out first, including the Voltage regulator, and the battery. It has been my experience that shops often rebuild alternators and fail to do a real electrical performance check to look for bad diodes and weak stator insulation. Consequently you can get a poor performing alternator from the dealer (I have) and get sent way off track troubleshooting the problem because you just can not believe the "new" alternator could be the problem.

Good luck, Jim

__________________
Own:
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles

Owned:
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)