Do you hear any sounds when you try to eject the disk?
The first way to eject the disk would be to drag it to the trash but as it does not appear on the desktop, that really is not an option.
A normal restart may result in the disk reappearing on the desktop.
Another way is to press the Eject key on the Keyboard. If there is no Eject key, try the F12 key. You may have to use the fn key for this.
Another would be to restart the mini and hold down the mouse button immediately after the chime.
Keep the mouse button held down until the disk is ejected or the system completes the boot process.
If that fails, try this:
Launch Disk Utility
If the disk appears in the sidebar, select it and choose Eject from the menu bar.
if that fails, try this:
Launch Terminal. You will find it in the Utilities folder.
Once launched type;
drutil tray eject and press return.
Let us know how you get on
I have a mac-mini OS-X 10.4.11 and have a disc stuck in it with no icon on my desktop, none showing when I open HD and I don't see a hole on the front for a forced eject. I have restarted, held the mouse button down and pressed the eject key with no joy. The mac doesn't show a disc being inserted so what do I try now, took another disc and pushed on the one in it in case it was not all the way in , still no joy, help.