Battery icon, no lightning bolt, not charging
For the last few hours, my iPad has had a black screen with a battery icon showing 4 red vertical lines. There is no lightning bolt on the screen. However, if I remove the plug, a lightning bolt and charger symbol appears - so the iPad knows when it's disconnected. I've tried two different Apple chargers, two different outlets, and also the USB port on the back of my Mac. I've done the Home/Sleep button thing about 10 times, to no avail. It might even be worse now because the screen seems to flash between the white Apple logo, to a black screen, to the screen with the battery symbol and back to a black screen. Every so often, my lock screen will pop up for a milisecond. I've examined the connection at the bottom and I do not see any bent pins, lint or debris. Nothing like this has happened to it before.
Any ideas? I would really appreciate any help. I've read through so many threads here, but haven't really seen anything quite like what's happening.
iPhone 4S, iOS 6.1.2, iPad 3, Mac OS X 10.7.5