Did you disconnect the battery prior to removing and installing the replacement screen? Not doing so can cause the backlight filter to blow and the iPhone 6S is particularly prone to this issue. The best way to test for this is to shine a bright light on the screen immediately after powering on the device. If you see a dim image, the the backlight is defective.
This could also be caused by a defective screen, as the others have suggested. The way to test for this is to re-install the original screen. If the original screen works, then you have a bad replacement screen )or connection issue). If the original screen does not light up either, then you blew the backlight circuit on the logic board. This requires a micro-soldering repair and is not DIY.