iPad 2 not charging after iOS 7.1

My iPad2 doesn't charge after the iOS 7.1 update and is now inoperable. I have been keeping it plugged in with the supplied Apple wall charger. Also tried charging connected to my MacBook Pro. The screen remains black unless I push the home button. Then I see a battery symbol will a small red stripe (actually 4 thin stripes) on the left of the battery icon that indicates the battery is extremely low. It will not boot in iOS. I tried rebooting. I tried connected via iTunes on my laptop. I have tried doing a factory reset by holding down the power button and home button over 15 seconds. Nothing. I am thinking of unplugging the charger and letting the battery run down completely. Then plugging it back in and hope then it will charge. And then maybe I will be able to restart it. I don't see anyone say they tried this. I am not sure this is recommended. Or if it might cause damage. I don't have any data on the iPad I am worried about loosing.