What made you think you could run the a/c for 30 minutes on the battery alone? Actually your battery did pretty good, my wife did the same thing and killed our battery in 20 minutes. Had to jump start it and drove it for about an hour. You might want to take it in to see why the service engine light is on. Maybe the battery is damaged and won't recharge correctly anymore.

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'06 X5 4.8is, TiAg/black, cold weather pkg., comfort seats
'07 750Li, TiAg/black, sport pkg.
'05 Ford F350 silver met./slate gray, Lariat, 6.0 PSD, CC, DRW, FX4