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I dropped my iPhone 6 a while ago and the screen still worked. Yesterday I dropped on the table and it turned different colors and then it turned off completely. When I plug it into a charger, I heard it charging. How do I get it to turn on?

Try a hard rest (Home + Power for about 20s or until the apple logo pops up). If that is unsuccessful then open the phone and try reseting the screen connectors on the logic board. If it still isn’t working then you will need the replace the screen. See this guide for opening the phone and removing the screen from the logic board: iPhone 6 Screen Replacement