Unless the case is bent, screen movement will only move the cables supplying the screen with power and video.
In that case, I would first look carefully at those cables (usually 2, one flat and one wire) to determine if they are shorting out against the case. You will have to open it up. Removing the kbd might give u enough visibility but u may need to open more up or even remove the screen. It could also be that movement of the screen cables is interacting with the power circuit. In any case, your shutdown is either because the power opened or shorted creating an immediate power loss.