iPad is frozen, says needs backup, plugged in, locked, and on wifi. How do we get it going again, can't turn off, can't get to apps, what do we do?

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You might try a forced shutdown to begin with, hold down the top and home buttons together until the device shuts down, then restart it.

If your back up continually fails, you might try turning off back up on your mobile device (settings > iCloud > storage & backup) and then deleting the backup file from iCloud by swiping the backup file on the mobile device (settings > iCloud > storage & backup > manage…) and then turning back up on again.

Being able to back up to the cloud can be very useful, especially if you don't have access to a computer or have infrequent access to one, however unless you specifically need to use iCloud for back up, you will find backing up to iTunes significantly more convenient and possibly more reliable.