And once the battery is checked and or replaced, buy and install a block heater and a heated battery wrap.
I struggled with my SD for two years before I finally installed the two items. Should have done it as soon as I bought the car.

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Thank You!
Fred
2009 ML350
2004 SL600
2004 SL500
1996 SL600
2002 SLK32
2005 CLK320 cabrio
2003 ML350
1997 C280 Sport