Battery could be defective. Try to stop by an at&t store and see if they can hookup your phone to their test device and go from there. If a new battery is needed, I would recommend contacting LG directly first to see if they could send you one. Also you might be able to get it cheaper through Amazon or eBay if you can't get free replacement through LG or at&t!
If your phone is over 2years old, thern your battery is shot
I don't know you would need to contact your Att store or go on line
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