Parts of iPad screen not responsive to touch in some apps

Two days ago my iPad Mini (2012) running iOS 9.3.1 started behaving oddly - moving from app to app, randomly opening windows and jumping from screen to screen of its own accord. In addition, in Safari, it started opening new tabs one after the other until it ran out of tabs. I thought maybe it had got a bug or something even though I hadn't visited any unusual sites. I did a reset, several times, which changed nothing, then I did a hard reset. Finally I restored the iPad from a backup. This fixed the jumping around issue but NOW I have a new issue - the corners of the screen in Safari, where you tap the back button, will not respond - also you cannot tap into the address bar i.e. at the very top of the screen. Rotating it fixes the issue, but then not able to type numbers as you have to to tap the same part of the screen as the back button in the landscape orientation. In iBooks and in Facebook the issue is the same - if you need to tap on that part of the screen (corners or very top of the screen) - it won't work.

I'm out of ideas! Anyone else had the same issue? (I've cleaned the screen as well.)