So right click on your desktop and select properties. Click on the Settings tab, and experiment with different Screen resolutions. You may not be able to generate 1920 x 1080, but maybe a different selection will yield better results for your display.
Also, try clicking on the "Advanced" button and looking at the options in there... if you have special drivers for your video card, make sure they are installed and updated. Sometimes there will be TV-specific output settings. If the video card is nothing special, you may try also "forcing" different resolutions by unchecking the "hide modes that this monitor cannot display" check box.