Also the battery could be completely discharged. What happens on the screen when an Apple cable in plugged into power?
Although, I have seen at least one iOS device that needed to be fully discharge before it would work again. (The home button did not work)
The OTA update went successfully on my iPhone 6 Plus and iPad Air but my iPad mini retina was stuck in the Apple logo and needed a restore. Fortunately I plugged in the device a day ago and there is an iCloud backup.