"slower sounding start" with a new battery and recent killed battery almost always is the starter. "The guy" unless he measured the current draw is speaking out of is butt. I've seen at least four cases on xoutpost in the past year of a worn out starter drawing more current than design by a LOT. The symptoms are: cranks a little slower than usual, hard starts when cold especially, battery gets low easily causing some odd need for a jump start.
I think the diesel draws about 250A normally. I've been working on a system to measure the starter current by measuring the voltage from the cigarette lighter to the B+ I just need to know the scale. I did the measurement once just as proof of concept and of worked great.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)