- Also try DFU mode after try recovery mode
- If not successful and you can't fully turn the iOS device fully off, let the battery fully drain. After charging for an least an hour try the above again.
- If still not successful that usually indicates a hardware problem and an appointment at the Genius Bar of an Apple store is in order.
Your iPad 3 is young enough to possibly be covered by warranty (if not water damaged). I suggest taking it to an Authorized Apple Service Center to find out if it's water damaged.
Here's how to contact them: