iPhone 5 no longer responding to touch
I would recommend bringing the phone into your local Apple Store or using the official Apple repair site to send it in.
Sometimes, even when there is no obvious cause for screen damage, it can still happen somehow. This happened to a previous phone that I owned, I sent it in and the screen was replaced, fixing the problem.
None responsive touch coupled with visual lines on the visual display is indicative of a damaged lcd screen.
This can happen in numerous ways, but ultimately end up in a screen replacement which usually solves the issue 99% of the time.