The replacement screen is either defective or it or the phone was damaged during the replacement.
Turn the phone on and look at the screen in bright light. If you can faintly see anything on the screen, it means that the backlight isn't working. If you see nothing, either the screen itself, it's connectors and cables, or associated circuitry on the motherboard us defective or damaged.
Since the phone connects to and is recognized by iTunes, the basic circuitry is working.