iPhone 7 No Power after screen replacement

In theory if you replace the logic board with another working (non-icloud locked) one, it will work although you will likely experience reduced functionality with some components like the taptic engine, auto-brightness sensor, and the earpiece proximity sensor (the thing that turns the screen off when you hold it to your head during a call). To my knowledge those parts are serialized to each phone’s motherboard and unless you get the parts that originally came with the replacement board, you probably won’t be able to restore full functionality to those components.