It is a feature of LCD displays to show their best picture only at the recommended resolution, which is basically the largest image the model will display.
For analog output your choice will be to send out the image via 15 pin VGA (D Sub 15 / analog) to, more than likely, 1366 X 768 or it's closest relative, 1280 X 720. Most, but not all, current high definition TVs will only accept that high of a resolution through VGA input. It might screw up your laptop's image *if* it is not a widescreen model. That should not effect the LCD TV's picture at all. Check your owner's manual for the display resolution via component cables. My Panasonic plasma will accept a 1920 X 1080i through component, but it drops the resolution to 1280 X 720p through VGA...go figure. This is advice for an analog stream only. Satfrat's solution may work, you should give it a try if switching your output to VGA 1280 X 720 does not.
As far as a digital stream, I don't know about DVI or using a DVI to HDMI cable to send your signal to the television and how that could be done properly using a computer as your signal source. It obviously works with an upsampling DVD, HD DVD

, or Blu Ray player. Your owner's manual *should* have something about that information. If not, you might want to check
www.avsforum.com and do a search. You might even find information about your specific model rather than a generic answer.
OH, make certain that you have the VGA output set at a refresh rate of 60Hz. Unless you have a 120Hz LCD, nothing will be shown on the TV screen. I don't know enough about the 120Hz models to give you any advice except to read the owner's manual about recommended refresh rate(s).
Good luck and I hope that you can find a great solution,

Chris