That's a mechanical problem with the dvd player, and not something Ubuntu can fix.
It can only be opened using the trick of putting a pin in the small hole under the DVD tray
As far as running a dvd, it depends on what the dvd content is.
Firstly, you can see if the dvd is even readable by opening up the home folder(if you haven't moved things around the home folder is the first thing(after the dash icon) in the left side launcher; it looks like a folder.
After opening the home folder, you can look at the left-side pane and see a listing for Devices.
Even if the dvd is not opening, it will be listed in this Devices section.
If the disk is not listed, then the disk is not readable.
Now, if the disk is readable and listed in home folder, the next step is to make sure you have the codecs to read the disk.
This is all assumption on my part, as I assume the disk is a movie, so either open up the software center or run this command
The package is ubuntu restricted extras in the software center.
sudo apt-get install ubuntu-restricted-extras
Here's what else you might need to do