Both VGA and Component video are analog, so you need not worry about the analog=digital conversion.. The component video interface, depending on the TV supports, 480i, 480p, 720p and 1080i resolutions only... Before changing any settings in the Laptop, you should first enable the secondary display.. This is usually done by a combination of Function keys available on the keyborad of the Laptop... Depending on the brand, it may be Fn+F7 or Fn+F4.. Exact information on toggling between the primary display (Laptop screen) and the secondary display (VGA out) wil be available in the supplied user guide... Once, the secondary display is enabled, you should see the Laptop's desktop on the TV.. If you do not get a picture even after enabling the secondary display, then reboot the laptop while the TV is on. This should adjust the output resolution in the Laptop according to the resolution supported by the TV... If even this does not help, then try to adjust the output resolution in the Laptop for the secondary display according to the maximum resolution supported by your TV through Component video interface....
I hope this works :-)