Chosen Solution
about a week after replacing my screen and having no issues, the screen went black. I had not dropped the phone before that either. I opened the phone up and disconnected and reconnected screen and battery cables as if I was replacing the screen again. When I power back up the screen lights up but never gets to an Apple logo before going dark. The rest of the phone functions as it shows up in itunes, and responds to find my iphone pings. I tried looking through the forum but didn’t have luck finding a similar question with an answer
If you still have access to the original screen, you should re-install it to see if the problem remains constant (logic board issue) or not (defective replacement screen). When you did the screen replacement, did you disconnect the battery prior to removing and installing the screen? Failure to do so can damage the backlight circuit and sometimes it takes a while to come into full effect. You can check for this by shining a bright flashlight on the screen immediately after plugging the phone into an iTunes enabled computer. If you can see a dim image, the the problem is backlight related. You just need to figure out if it’s the backlight on the screen or the backlight circuit (see my first sentence). You may need to find a known-good screen if the original was completely faulty or thrown in the trash.