iPad mini must be plugged in to turn on even if battery is fully charged When I press the button to turn on the iPad mini it is asking to be plugged in despite the fact the battery is fully charged. Once plugged in for a few seconds I can remove the plug and the iPad mini will boot up fine.

iOS 8.3
Sometimes it helps to do a soft reset:
hold the Power button and the Home button at the same time, keep holding, the unit will switch off, keep holding, then when you see the white apple logo let go and let the ipad start up normally.
Try again.