Then head to the apple store if that fails. The iPad 4 was being sold until recently so there's a great chance it's still in warranty.
Bob
I have an iPad 4 that was working fine until the iOS 8 updates. After that, while I was playing Candy Crush one day the screen went kind of scrambly and the iPad shut off ... and wouldn't turn back on.
When I plugged it into my laptop, iTunes tried to do a recovery/restore but it remained stuck on the restore phase. A few days later I was trying again - iTunes got stuck. I disconnected from the laptop and plugged it into the wall and suddenly it was working! Hurray!
Everything seemed all well and good after that. Until one day, I was playing Candy Crush again and the iPad scrambled and shut off. Now nothing seems to make it miraculously turn on again 
Any help?
Chowhound
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GameFAQs
GameSpot
Giant Bomb
TechRepublic