My iPhone 4 screen is totally unresponsive

In the past I've had some issues with my iPhone 4 screen not responding to touch, but it's usually only for a second or two. This morning my iPhone screen was totally unresponsive to all touch - I can't even switch it off because it doesn't register that I'm trying to swipe to do so. I've tried a hard reset, I've tried letting it run out of battery and charge again fully but nothing works.

I backed it up and was going to a factory restore but can't even do that, as I have to turn off Find My iPhone and need to get in to my phone to do so. I attempted using icloud.com to do it but the error message still comes up in iTunes.

Any suggestions?