The problem is every time I click the button to open the disc tray, it never opens.
How do I fix this?
Hmm, you might need to get a new drive. In the meantime there should be a little hole on the front. If you get a paperclip and shove it in there it should pop right open. Hopefully whatever was stopping it from opening is now fixed, if not you may need to get someone to take a look at it or buy a new one.
You may have a hardware problem. Most optical drives have a small manual eject slot in which you can insert a paperclip or a toothpick to force the drive open.
What OS are you using? Some will refuse to eject a "busy" disk. Try the Eject option from with the Windows Explorer or Nautilus if on Linux.