LCD displays can sometimes show small pixel sized spots. These spots are visible as either white, black, red, green or blue dots on your display. The color of the pixel determines the problem or condition itself. Pixels can get (stuck) in a certain state, or become non functional (dead) LCD display panels are manufactured in a process that simulates a sandwich. A LCD glass panel contains millions of transistors, each the size of a pixel which is roughly 1mm square. These are further divided into red, green and blue, subpixels. A chemical compound called liquid crystal is sandwiched between plates of transistors which produce a lighted pixel. Millions of pixels are combined to create the image that you see.
Occasionally, a pixel can stop responding and appear in one of several colors. A black or white colored pixel indicates that the pixel itself is dead. This basically means that the electronic transistors for that particular pixel are not functioning.
Red, green or blue pixels indicate that the pixel is stuck. This also means that that pixel's circuitry is not functioning. A stuck pixel is not as serious as a dead pixel, and can very often be unstuck using various methods.
In the case of PC and laptop LCD's, there are various homebrew software utilities (homebrew is a term used for free software created by individuals for non commercial use) The pixel fixing software rapidly changes all the possible colors of the pixel in a repeating cycle until the pixel responds and becomes unstuck. A similar process also is used for dead pixels, however not as likely to repair the problem.
If you have a LCD TV, you may be able to connect it to your laptop, and utilize the same pixel fixer software. Please - use at your own risk! Some manufacturers include options built into the lcd's menu and setup utilities. Otherwise you may have to contact the manufacturer for assistance.
It is quite common for brand new LCD panels to have one or several pixels stuck or burned out. Of course this is very disappointing and is a cause for concern. Each manufacturer and retailer has different criteria for acknowledging this type of problem and dealing with it. It is not uncommon for a LCD panel to have ten or more dead pixels before the retailer or manufacturer will consider a warranty replacement. Personally, one dead or stuck pixel in a new display is too much. You should check with the retailer before you purchase an LCD panel to understand what their return and replacement policies are in this regard.