I've had several do that, including two on a couple of my AIX machines at work. The rubber belt that runs part of the opening mechanism breaks when they get old. I've heard a rubber O ring, found in the plumbing department of most home improvement stores, can replace them, if you get the right size.
Use the manual eject hole to open the drive, mentioned above, and see if you can find a small wheel right in the front center of the drive under the eject tray, and if it has a rubber belt on it or broken and nearby. If you can get that belt out and bring it to a home improvement store, you might find an O ring to use to replace it. I have only heard about this, and not done it myself, but I plan to in the near future.