The track for the disc tray must have come loose or broke with the fall. You might be able to get it open (in case you ha a game in there) with a gentle pry on either side of the tray.
After looking around my own "fatboy" PS2 i could only see one screw on the back on the tray side. It may be simpler (and cheaper) to pick up a slimline model instead of repairing this one.