I have a kind of similar problem and i restored the factory settings and uploaded the latest iOS. But the problem persists. The IPAD starts and then it dies again. The battery indication says that the level is low - I charge for long time but the same problem again, it will go down after 2-3 mins? The local apple shop quoted 350 EUR for repair! Now the tech dept of the shop i bought it from investigates. Appreciate your feedback since i am very unhappy that little over one year i bought i face such problem.