iPhone is black and won't turn on. Could this be the problem?

My Iphone 5c won't turn on.. I have tried holding the home and on/off/powerbutton down, changing my charger, connecting it to itunes. (Itunes can feel a phone connecting but the phone is still dead).

I got my bf to open the phone to and see if everything was alright inside, and we saw this. (look at the photo).

It looks like a part of the phone melted nearby the battery? could this be the problem and do anyone what that might cost to repair?

I have a new phone and only need the photos from my world trip from this one, and hope it isn't too expensive to repair...

Hope anyone have seen this type of problem before