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An iOS device will always go into DFU mode. If it doesn't then it's either user error or a hardware error.
 
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)
 
My 2 friends iPhone 5S had problems when it came to OTA update.

The screens went black for roughly 15-20 minutes, on clicking the home button it would say 'verifying update...'.
 
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. :rolleyes:
 
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