Your dead pixel might actually be a stuck pixel.
Wikipedia: Stuck pixels, unlike dead pixels, have been reported by LCD screen owners to disappear, and there are several popular methods purported to fix them, such as gently rubbing the screen (in an attempt to reset the pixel), cycling the color value of the stuck pixel rapidly (in other words, flashing bright colors on the screen,) or simply tolerating the stuck pixel until it disappears (which can take anywhere from a day to years). While these methods can work on some stuck pixels others cannot be fixed by the above methods. Also some stuck pixels will reappear after being fixed if the screen is left off for several hours.
Either way, it seems like there are several possible techniques you could try to fix this.
- Pressure method
- Tapping method
- Heat method
This howto shows these techniques step by step and has a good explanation of the process. Hope one of these techniques can help out
There are several several software-tools you could use to remedy this as well.