My iPad 2 has suddenly stopped responding. I had put it to sleep by closing the cover, and when I opened it, the screen was black. There have been no drops or other obvious mistreatment. So I held down the power button, ostensibly to shut it down. No response. Held down the button again, ostensibly to start it up: no response. Tried that many times with same result. Charged the iPad overnight. Still no response (and no little chime sound that usually happens when I plug in to AC power). iTunes can see the iPad, so maybe the screen is dead. But with the absence of all responses of any kind, I'm wondering whether it's worse than that. I'm running iOS 7.0.4, so I suppose I could update to 7.0.6 and see if that helps, but since updates can be dodgy, I thought I'd save that as a last resort. (And yes, my AppleCare coverage is history.) Any thoughts?