By the look of it your laptop may have an Ati or Nvidia mobile graphics chip inside it.
I would advise you to name the exact brand and model number of the laptop so we can see if it is the case.
The problem with laptops is this, all of the chips use what we call a BGA, ball grid array.
Things like the graphics chips are soldered onto the motherboard of the laptop this way.
But due to heat and time the little balls of solder melt and become unseated or end up with bad contact to the board.
The end result is colored dots on the screen or colors not displaying right.
A re flow of the chip on the board is often required to fix the problem.
However you can in some cases also get this problem due to the video cable from the motherboard to the Lcd screen causing it.
As the video cable is passed through or near the hinges that allow you to fold the screen up and down pass through this area. So the video feed cable suffers damage.
Time and age plus heat are the causes for both.
Both will require an extensive strip down of your laptop.
If you feel you can do this at your own risk. Or sent it to someone who can for you.
The last resort is to send it back under warranty of course, if it has not run out so i would check that first if the laptop is less than a year or two old.