Chosen Solution

Hello, I tried to replace the screen and because the screws of the metal board near the battery connections were not coming out easily, I scratched the black surface of the logic board as you can see. http://prntscr.com/oj4wqt I didnt go through with the screen replacement and assembled it back. It wont turn on. Was this black coating important and why? Is it the reason why it doesn`t turn on anymore?

The surface you scraped is fine. You need to remove that last screw on that bracket. Maybe a better tri-point driver is what you need. Once the bracket is removed make sure all the connectors are seated properly. Does iTunes recognise the phone? You might have damaged the lcd flex cable while trying to remove the screws. Go ahead with your screen replacement with the ifixit guide and all should be good.