I know on mine (D503) which looks almost like the same exact mechanism, there's a cam lock on the bottom side which is driven by that belt motor/ gear assy. If you take the cover off which is easy to do with 4 screws on the side and 3 shinny screws on the top back then the lid comes off and you can push the tray out carefully if you know what to do.
Also a good time to look and see if its dirty/ dusty, etc.
Pics are worth a 1000 words