Try refitting the front facing camera. The camera flex also has a microphone which is used for videos ect. Make sure the microphone is lined up correctly on the rubber gasket and that you have removed the small piece of plastic that keeps the adhesive sticky on the gasket itself. If after that it doesn't work, just replace the camera flex.
Is the screen cracked in any way? Have you dropped it? Any pressure been applied to the screen? The lines indicate that the lcd is damaged. The top portion of the lcd underneath the glass is very fragile so possibly that has been damaged in some way. Cheap enough to fix if your competent and not too expensive to get a repair shop to do it.
Is it definitely powering off or is the screen going blank? Try connecting it to your pc with the screen attached but not installed fully, then try and fit the screen, you'll know if it's powering off because your pc will make the usb disconnected noise. If it's still on then the new LCD ribbons might be be damaged.