When I had Windows (XP x64 or 7 64-bits) installed on my computer, my LG super multi drive worked fine. But now, with Ubuntu 10.10 64-bits, this drive doesn't work. When I click on the physical button to eject the drive, nothing happens.

Can anybody help me with this?

So you are not even able to open the drive when running Ubuntu?
You can open a terminal and run: "sudo eject" and it should eject the drive. If sudo eject gives you errors, then post them here.

EDIT:
If sudo eject gives you errors, try running "sudo eject /dev/sr0" and it should work.
I just tried running sudo eject on my Lubuntu 10.10 and it did this:
When I ran sudo eject /dev/sr0 the drive opened. I am able to open and close the drive manually also.
To verify that the drive is still working, try booting into the computer's BIOS and verify that you can open and close the drive.
EDIT2:
Assuming you can get the drive open, then try changing dev/cdrom in any media program to /dev/sr0 in the program's preferences menu. I had to do that in Asunder to get it to recognize my CDs.
Hope this helps.

I've just figured out what was wrong: the drive was not connected to the PC nor powered by the power supply. I thought this couldn't be the problem, because I never messed with the cables connected to the drive. Now that I think of it, it was probably the people from MisterPC (Informatics Technical Assistance) that did this when they were trying to figure out the problem I had with my PC that made it reboot on its own that I had a few months ago.

All electrical equipment works much better when plugged in!