When you output to the TV then you are running a different res (1920x1080 - HD). When you fire the game up, it then reverts to the laptop res as output which is 1440x900 and I doubt whether your tv supports that res.
Best would be to check your tv manual to see what res it supports and then adjust the game to that res.
As to getting your tv to display again - right click desktop and select properties. Then go to settings, click monitor 2 and adjust the res to 1920x1080. When the game launched it actually made the monitor 2 res = to the game's res.