The arduino is simply not powerful enough to interface with such a screen. You would need a lot of seperate hardware to run the screen and act as a frame buffer.
It is possible to get boards which allow laptop screens to be connected to via VGA in which case you could get a low resolution B&W image using the timer modules, but really an Arduino is simply too slow for such a screen to get any decent resolution/colour.
Just as an example of how much data there is:
A standard 17" laptop screen has a resolution 1440 x 900 = 1296000 pixels per frame
At a standard 24bits per pixel that yeilds: 31104000 bits per frame
A normal LCD refresh rate of a laptop screen is around 75Hz = 2332800000 bits per second = 2.17 Gbit/s = 278MB/s
An arduino has a clock rate of 16MHz, so that means the ideal data rate for the screen is 2.17G/16M = 145.8 times faster than the Arduino clock.