I had this same issue. After replacing a cracked iPhone 6 Plus screen assembly, iTunes recognized the phone when plugged in, but screen was completely black and not working. I tried several screens, including installing the original cracked screen back and still seeing the same issue.
SOLUTION: I disconnected the battery and the screen and examined the screen assembly. Noticed that the plate holding the camera in place was not exactly even. Unscrewed the plate holding the camera assembly. While removing one of the screws holding the camera assembly plate, I noticed it came out with a small piece of battery adhesive. I took the adhesive off the screw, and replaced the camera assembly plate. Connected the 4 screen cables, connected the battery, and the apple logo appeared on the screen.