Screen not responding to touch, image ghosting/retention.

I've hard reset my phone and performed a full erase/restore. The touchscreen will work initially, and then eventually stop. Parts of screen images will seem to burn into the screen (retention/ghosting). This all resets for a bit if I turn the screen off and wake it back up. Images are normal and touch works for a bit (minute or less) then the above starts happening again. There will also be light vertical artifacts on the screen, like bars.

It currently has iOS 9.0.2 installed.

Phone has been dropped a few times (not recently) but was always in a protective case. It hasn't gotten wet.

Trying to get some input as to what needs to be replaced before I start throwing money at parts.