Start by testing alternator output voltage. If it's above 13.5 or so, it's probably fine.
The battery will not stay over 12v for long once the alternator is off it.
If the alternator is good, disconnect the battery and see if it discharges overnight while not hooked up to anything.
Or, as an alternative, take it to an auto parts store and ask them to test it. The gigantic, expensive battery conditioners that they have can rehabilitate a battery that home chargers can't.
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2011 M3
2006 Sierra 2500HD 4WD LBZ/Allison
2004 X5 3.0i 6MT
1995 M3 S50B32
1990 325is
1989 M3 S54B32
Hers:
1989 325iX
1996 911 Turbo
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