Is my system Certified or Tested with Ubuntu?

"I wanted to know if my computer will work with Ubuntu"

The short answer is:

http://www.ubuntu.com/certification

The longer answer is:

To determine if your system is compatible with a certain version of Ubuntu, please see the site listed above.

http://www.ubuntu.com/certification is the official list of certified client and server systems that are tested by Canonical for each Ubuntu release. Those systems are "Officially" certified, tested and supported with a given release.

Finally, if your system ran a previous version of Ubuntu, then most likely it will run the most current as well. Of course, this is NOT a guarantee of any sort, as there are sometimes changes between releases that cause problems for older systems that used to work well. In those cases, filing a bug would be appropriate.