When I replaced my friend's 5s display, it would go red then reboot. I fixed it by doing a hard reset by holding the home and power buttons, you can look it up. Sometimes the phone doesn't "recognize" or work with the display right away. Doing a hard reset re calibrates, not sure what the actual term is, the display so the iphone recognizes it and will boot. Hold power and home button together at the same time for 7 seconds then let go of home but keep pressing power. I only know of this from when I replaced my iPod touch 4th gen display and the guide on ifixit had a note mentioning it.