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Yes, that is a software problem. It is reported that some devices are getting corrupted after or while doing the update. By hard shutdown, did you mean reset ?
If you have not done thta already, please do the reset. Press and hold down the Power button and Home button at the same time until it shows the Apple logo. When you see the Apple logo, release the buttons and let it boot. Then try to update.
If that didn't work, then you have to restore or update the iPhone using your computer.
First download and install latest iTunes on your computer from here : https://www.apple.com/itunes/download/
Then connect the iPhone to your computer with the USB Cable.
Open iTunes application on your computer.
iTunes will recognize your iPhone. Select your iPhone in the top left (select iPhone icon)
Then in Summary section, click Update button and let it update.
If your computer is not recognizing the iPhone in iTunes, then you have to restore the software of your iPhone. Restoring will erase everything from it unfortunately.
Make sure latest iTunes is installed. You can download and install it from the above link.
Connect the iPhone to your computer and open iTunes.
On your iPhone press and hold the Home button and the Power button at the same time until your iTunes shows a message telling you that it has detected an iPhone in recovery mode.
Click Restore. It will take a while to restore it.
Let it restore. After restoring, you can restore the backup of iPhone from iCloud which will restore your data. Please let me know if that didn't work, so we can continue troubleshooting
Remember, this is not my final answer. If my solutions didn't work please don't rate me bad or poor. Instead please reply back to me and I will continue to help you until we fix the problem or you are satisfied.