3 Answers
3

I think it is impossible to economically fix that screen.  Effect you are seeing is caused by breaking conductors inside the screen.  Basically, TFT screens have horizontal and vertical conductors inside for each row and column of pixels (second image on the link).  Once the connection is cut, pixels from the break point are uncontrollable.  If you press the screen in certain places, you might temporarily restore function of some pixels, but as soon as pressure is removed, they will go off-line. 

Yes, I've replace a screen myself.  As long as you follow instructions (and don't lose a small screw in the process), it's quite straightforward. 
–
sleskeApr 21 '11 at 8:16

Also, be aware that an official (i.e. from the manufacturer) replacement LCD screen is often prohibitively expensive.  But people often sell old, functioning screens on eBay etc. ( or just buy a broken laptop with an undamaged screen). 
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sleskeApr 21 '11 at 8:17