First disconnect the battery. Not unhook the screen and check the pins on the connectors on the screen and motherboard for any bent pins. Clean the connectors with a qtip and alcohol and a soft brush. It's possible that it's a bad connection. Also verify that that the image is there buy really hard to see because of back light. Is there is a possibility that you damaged the backlight circuit when you changed the logic board.
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=== Update (07/23/2020) ===
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It sounds like you blew the backlight circuit and possibly the touch on that half of the screen. Did you disconnect the battery before you changed the screen? It's a common problem that people don't disconnect the battery and it shorts out the backlight circuit. You will need to take it to a repair shop who can microsolder.
First disconnect the battery. Not unhook the screen and check the pins on the connectors on the screen and motherboard for any bent pins. Clean the connectors with a qtip and alcohol and a soft brush. It's possible that it's a bad connection. Also verify that that the image is there buy really hard to see because of back light. Is there is a possibility that you damaged the backlight circuit when you changed the logic board.