It might be the rubber belt inside that's loose or worn out. You might be able to replace it without taking apart the drive completely. It's just underneath the tray.

Some client of ours had this same kind of problem, drive bay won't close. We just replaced it with a belt of the same size. We bought it from some electronic shop. Then it was ok. The tiring part was looking for the exact size. It would be good if you can bring your drive's rubber belt with you and look for the same size.