Any constant drain will kill a battery.

Disconnect the alternator.

Post the last seven of your VIN so we can look at the real oem and determine which alternator.

The m62 I've worked on had water cooled models and not terribly difficult to r & r. Comes right out the front only difficulty usually is to remove the radiator fan

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