I purchased my brand new IPAD 3 2 weeks ago. I've tried to charge it using the wall socket and left it overnight. It actually lost charge (33% down to 28%). BTW it did not display the Not Charging message.
I tested the power point and it works for other appliances. I plugged the IPAD into my laptop via the USB port and got the message Not Charging.
Last week I did manage to charge it, albeit not fully and it did take a while.
Do you think there is a problem with the battery?