Q: iPhone 6 display now becomes unresponsive after updating to 9.3.2

VT Baker wrote:

...do i need to erase the phone again and start it as a new phone?  can i then restore it from a back up to get all of my data back?  any help would be great.

You may have to do a system restore based on what you describe. If the backup is corrupted, a real possibility, you may have to set it up as new. A lot of hassle, I know.

System Restore. First backup your device using iTunes. Also import your photos to your computer and copy all important data. Try restoring from backup first and testing it. If it does not help, you may have to restore as New and reconfigure from scratch as the backup could be corrupted. For this reason it is important to have your photos and data saved separately from the backup. Here are the steps for a Restore:

https://support.apple.com/en-us/HT201252

If the above steps do not help, you may have to have it tested at an Apple Store.

Yes, you can restore a backup after restoring the phone to factory settings.

Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support

You can also try erasing all content and settings and then restore a backup and see if that works.

How to erase your iOS device and then set it up as a new device or restore it from backups - Apple Support

Unfortunately some backups can be corrupted if the underlying apps or settings are themselves corrupted. Restoring as new is a pain as all settings and apps would have to be configured from scratch. Good luck.