My phone has had the screen and LCD replaced, but black screen

If your phone is recognized by iTunes, that means the logic board mainly works. As for the "black" screen, you either have a backlight issue or a dead LCD.

To check the backlight, connect your phone to iTunes and shine a bright light on the LCD. If you can see a dim image, then the backlight is the issue.

If you suspect an LCD issue, you can go in a dark room (or wait until darkness) and turn on your phone. If the backlight appears to be on, even if the screen is black, then you may have an LCD issue.

Either way, the likely suspect here is a defective replacement screen. If your original, presumably cracked screen is still available, you could try re-installing it to see if it lights up properly. If it does, then you need a new replacement screen. If it doesn't, then the backlight circuit on the logic board may have been damaged (i.e. the battery plugged in while replacing).