Perfect image on screen but not responding to Touch

I need help identifying which part(s) are damaged so I can purchase them and attempt to repair.

My iPhone got wet inside a backpack under pouring rain. It was On at the moment and by the time i realized it was wet, I had already pressed the home button. I turned it off and left it to dry for a long time, did the bag with rice for several weeks. When I first tried to turn it on after probably a month, it charged fine, image on screen looked crisp but acted as if a ghost were touching the screen, it kept opening and closing apps like crazy. It would respond to my touch when I selected options and apps but it would keep going even when not touched at all.

I turned it off and let it be for a couple more months. I tried again this week, charged like a charm and retained charge for a couple of days, images still looks perfect but now touch screen would not respond at all. Could not turn it off as it wont recognize me sliding the bar to confirm power off. Home, sleep, volume and ringer off buttons appear to be working fine, showing appropriate images on screen when operated. The glass is undamaged and the phone has not received any impact.

What part is likely to be damaged and how do I replace it?

I appreciate your help