I have had my iPad 2 for a year now and have recently run into problems turning it on. After charging fully, it will sometimes turn on, showing a full battery, however after leaving it idle for about 10 min, it turns off. If I use it for an extended period of time, it stays on with the battery decreasing in charge as it normally would. When I then reconnect it to the charger, it will (sometimes) turn back on after a cold reboot. Are these symptoms of a dead battery, or something else? If I can provide more info that would be helpful, let me know-- Thanks!!