I might be inclined to run a piece of wire from the breaker box to the GFI plug and connect it that way. If that makes the GFI stop tripping, then disconnect the ground from your temporary wire and use the ground in the plug box. If it trips, it's the ground wire. If not, connect the neutral in the box. It it trips now, it's the neutral. Next try the hot in the plug box and the neutral in your temporary wire. It might just be a loose connection for the neutral wire in the panel board.
It's a process of elimination using a piece of wire along the floor instead of the wires in the walls.