If it does try to eject the disc but fails, then it might be getting caught in the opening. This is particularly likely if the disc has a stick on paper label (very bad idea in a slot loading CD drive).
If it is trying to eject (you should hear this) and getting stuck a trick I have used successfully in the past is to get a sheet of paper and push the corner of the sheet in to the drive opening. What you are trying to do is use this sheet to sort of act as a guide to the CD so it lines up better with the slot. It also helps hold down the dust exclude strip which might be getting in the way.
You could also on your model in theory remove the top of the Mac mini case so the CD/DVD drive is exposed and plug the computer in (without its top) turn it on and again try ejecting.
If the computer is not trying at all to eject the disc then the mechanism may be totally dead and need replacing (I had do this recently).
Well Unfortunetly I have no icon showing up on my computer, I have tried restarting with the mouse held down and it is not making any noise like it is even trying to eject the disk. I hope that I don't have to replace it but it is kinda old. Any other brilliant ideas out there?
That is what happened with my drive which I ended up having to replace.
What you could try doing first is to take the top of the Mac mini case off, then see if you can spot anything in the CD/DVD drive that is stuck. If not then you could take the risk of trying to take the top metal plate of the CD/DVD drive off to expose the disc and see if you can 'help' remove the disc and then reassemble it. Unfortunately while in my case this got the mechanism moving again it would not read disks so I had to replace it. I got one off eBay.
check out Kappy's user tip:
Five ways to eject a stuck CD or DVD from the optical drive
Ejecting the stuck disc can usually be done in one of the following ways:
1. Restart the computer and after the chime press and hold down the left mouse button until the disc ejects.
2. Press the Eject button on your keyboard.
3. Click on the Eject button in the menubar.
4. Press COMMAND-E.
5. If none of the above work try this:
Open the Terminal application in your Utilities folder. At the prompt enter or paste the following: /usr/bin/drutil eject.
If this fails then try this:
Boot the computer into single-user mode. At the prompt enter the same command as used above.
To restart the computer enter "reboot" at the prompt without quotes.
i stuck a credit card in... it kept cycling trying to eject. after a few mins as i was about to type out a nasty gram to apple to complain about the issue as my computer is only 30 days old, it finally ejected. i had the card about half way in, dead center of the disk. i did this to stop the disk from spinning. it will eventually allow the disk to be ejected and guide right over the card.