If your LCD screen has a stuck or dead pixel (a point on the screen that is always lit or always dark), it is usually due to a transistor malfunction or uneven distribution of liquid in the liquid crystal display (TFT LCD). This can often be fixed.
Steps
Pressure Method
Turn off your computer's monitor. Get yourself a damp washcloth, so that you don't scratch your screen.
Take a household pen, pencil, screwdriver, or some other sort of instrument with a focused, but relatively dull, point. A very good tool would be a stylus.
Fold the washcloth to make sure you don't accidentally puncture it and scratch the screen.
Apply pressure through the folded washcloth with the instrument to exactly where the stuck pixel is. Try not to put pressure anywhere else, as this may make more stuck pixels.
While applying pressure, turn on your computer and screen.
Remove pressure and the stuck pixel should be gone. This works as the liquid in the liquid crystal has not spread into each little pixel. This liquid is used with the backlight on your monitor, allowing different amounts of light through, which creates the different colors.
Tapping Method
Turn on the computer and LCD screen. Display a black image, which will show the stuck pixel very clearly against the background. (It is very important that you are showing a black image and not just a blank signal, as you need the backlighting of the LCD to be illuminating the back of the panel).
Find a pen with a rounded end. A Sharpie marker should be fine for this.
Use the rounded end of the pen to gently tap where the stuck pixel is - not too hard to start with, just enough to see a quick white glow under the point of contact. If you didn't see a white glow, then you didn't tap hard enough, so use just slightly more pressure this time.
Start tapping gently. Increase the pressure on the taps gradually for 5-10 taps until the pixel rights itself.
Display a white image (an empty text document is good for this) to verify that you haven't accidentally caused more damage than you fixed.
Software Method
Try running pixel fixing software (see external links). Stuck pixels can often be re-energised by rapidly turning them on and off. If this fails, complete the following steps.
Tips
Many people report success with this technique but these instructions won't work in every case. It may take a few attempts to make sure you are pressing exactly on the dead pixel. These instructions will fix "stuck" pixels, not "dead" ones. Dead pixels appear black while stuck pixels can be one constant color like red, blue or green.
An alternative, but similar technique involves gently massaging the stuck pixel with a warm damp (not wet) soft cloth.
Alternative technique to tapping: Using a rounded pencil eraser, push with moderate pressure into screen at stuck pixel.
If these instructions don't work, you can hopefully get the monitor replaced through your manufacturer. If your monitor falls under the specifications of replacement, get in contact with the manufacturer to set up replacement plans.
Warnings
Do not attempt to open the monitor as it will void the warranty and the manufacturer will not replace it. Make sure you don't get any electrical equipment wet or it may break. Some people claim that touching the screen can cause more pixels to become stuck, although this has not been proven.
