Touch screen unresponsive for iPad mini

I have an iPad mini 32GB running iOS 8.4.1.

The touch screen is unresponsive - cannot swipe to log in, etc. Everything else seems to be working: the screen displays the log in prompt, I can reboot by holding down power & home buttons, I can connect to a Mac & upload / download data & programs.

Went to Apple Genius. They tried factory reset - this didn't work.

My question here is which component is likely to be messed up as I would like to try repairing this using one of the guides. My first thought would be to replace the LCD, but I don't know enough about iPads to know whether that's likely to be the source of the current problem.

Any help / advice appreciated.

All the best

Richard