Thanks for the replies, tips and links.
I've checked out a few videos and solutions. A lot of them seem to be on Macs which have an 'eject' button. I've never used a Mac before, so I figure only the new Macs have no eject button at all.
The disc goes in, an icon appears on the right of the screen (desktop) and you have to click the icon and choose the 'eject' option to eject it.
Currently there's no icon on my screen (no surprise), so there's no option to eject or start the 'eject' motion. I'm not sure if the mini disc is all the way in or just somewhere halfway. I don't think replacing the whole optical drive is a good option, especially for a computer a few days old.
I guess I'll read on and see if I can find better ways...