Are you using Nvidia's proprietary driver? I doubt that you will be able to get HDMI working unless you install the proprietary drivers.
Getting them installed can be a little tricky, but the first step is to head on over to Nvidia's driver download page and enter the appropriate information:
For example, if you are using the 32-bit version of Ubuntu, you would select "Linux 32-bit" and download this driver.
Once the download is complete, open a terminal in your downloads directory and run:
chmod 755 name_of_downloaded_file
...to make the file executable and then:
...to launch the installer.
Update: I totally forgot to write the instructions for actually enabling HDMI output. Run the following in a terminal:
This will launch Nvidia's configuration utility. From there you need to click, "X Server Display Configuration" and click "Detect Displays" (assuming the HDMI cable is plugged in). Then it's simply a matter of configuring the display as per normal and applying the changes.