This video shows how to fix the tray of a CD or DVD drive when it does not eject after pressing the eject button.
Most of the times this problem is caused by a dried rubber band in the eject mechanism.
The solution is simple: Open the drive, replace the rubber band, and that’s it. Watch the video for details.
If none of this worked you may consider buying a new DVD drive. Here’s a link to a reliable online store: http://amzn.to/19BamPr