Chosen Solution

Where the screen connects to the logicboard looks a little melted. The phone had water damage but the screen needs to be replaced. So I’m waiting on the part. They old screen seems to still connect Update (08/05/2017)

This is the melted part I was talking about.

If you mean the stuff around the connector, that is the waterproof seal. It is supposed to be there to protect the connectors.

There is nothing melted here. Your backlight filter looks damaged and there is water damage on the board, but the connector is not melted.