Its generally called a 'stuck' pixel. There is some software that could fix it, a quick google search will turn up many options that claim to be able to fix some stuck pixels but not all can be fixed. My emachines got one within 2 weeks, i tried many options but none of them worked.
If you can dirty up the spot on the screen where the pixel is, then turn off the monitor. Then gently press something with a small point thats soft(soft pencil lead with a few pieces of papertowel on the tip) directly on the spot with the stuck pixel. Not too hard, but you should feel a very slight give.
Turn on the monitor and it should be good for a few months. It's what I do with mine.