The most common causes for iPhones that seem "dead" after screen replacement are the following, as we've seen them and fixed them in our workshop:
1- No display (no image) or no backlight (extremely dim image), due to using a defective part or damaging it during install. iTunes should see the phone. A replacement screen should solve the issue.
2- No display, due to long screw damage = mixing screws on the plate that secures the screen cables. iTunes should be able to see the phone as well.
3- No back-light, due to damage to back-light circuit during screen installation. iTunes will see the phone.
4- Phone is dead due to using metal tools and causing pry damage or a short. Should not be detected by iTunes.
Whatever the cause, apart from "1," you need the help of a micro soldering technician to repair the phone.