My iPad Mini won't turn on after charging
If you are not near an Apple store or Authorised Service Provider then call up AppleCare (apple.com/contact) and they will help you try a few steps and if they come to the conclusion that your iPad needs to be swapped then they will send you one. Pretty sweet deal. I encourage purchasing AppleCare+ as well while you talk to the phone agent because you have a small period of time to purchase it and it is a fantastic investment.