Before we begin, we need to understand what exactly is a dead pixel on your laptop screen. A dead pixel, by definition, is a dot of display on your lapotp screen that remains unlit. These dead pixels are usually best seen against a white background. They are usually caused by manufacturing defects and manufacturers have a clause to say a certain number of such pixels are permissible in a brand new laptop.
 

An example of a dead pixel on a laptop screen

A good thing to do, if you suspect that your laptop has dead pixels, is to use a dead pixel test program like Dead Pixel Buddy. The program has a wizard which will step you through display of different background colours on your screen so you can see which dead pixels are present. This is useful if you want to prove to the manufacturer that a dead pixel exists.

Every laptop manufacturer (the more well known ones at least, like Toshiba, Lenovo, Dell, Apple, etc) has a 'dead pixel policy'. For example, if you have more than 7 dead pixels in your Dell laptop, you can approach Dell to have it replaced. If you have more than 3 dead pixels in your Fujitsu laptop, you can get it replaced. So the policy differs from manufacturer to manufacturer. It even differs between retail shop to retail shop. So check carefully before you purchase the machine.

We've spoken about dead pixels - but be aware that there are things like stuck pixels and hot pixels too. A stuck pixel is most visible against a black background, where it will might appear red, green, blue, cyan, magenta, or yellow. A hot pixel is a permanently lit pixel and are more obvious against a black background. Technically, a stuck or hot pixel is not considered a dead pixel. So in checking your manufacturer's policy, you might also want to ask about stuck and hot pixels too (most of them don't cover these defects).

There is usually no way to fix a dead pixel. The reason is that this is usually a hardware defect. Stuck pixels can be corrected using software - there is a program called JScreenFix that flashes numerous colors with a very rapid intensity onto your screen. You can also correct stuck pixels by gently rubbing the affected pixel area.