You probably have a broken wire going from the video card to the LCD screen. I was a laptop tech with NEC and have seen this many times. If you move the screen back and forth, does the color change? What if you press down on the laptop near the base of the LCD screen? Personally I would dissamble the laptop top find out, but I doubt most people are that brave. Do you get all of your colors fine when you plug an external monitor into the back? If so, then that would seem to indicate the Video card/chip is ok and that is likely just a wire. LCD's dont just lose one color like a monitor. With a monitor you have 3 color guns. With an LCD you have transistors. If a transistor went out, you would get a dead pixel. This would look like a Black, Green, Blue or Red dot. I think its a wire, and if that is the case you would need to have the manufacturer of the laptop fix it for you. I am sure they will just swap out the LCD assembly (including the wiring harness for the LCD, and its expensive if you are out of warranty!!) and call it good.
Good luck!
-t