This problem has been going on for some time and I have never quite been able to figure out why.

At random points throughout my time on my computer, my monitor will go black as if it's going to sleep. If I was typing anything, anything I typed in the 1 second or so that my computer blacked out doesn't show up on the screen, so I can tell my computer is unresponsive for that 1 second. The same goes with clicking anything, if I happened to be clicking a link at the very second it blacked out, I didn't navigate away from the current page I was on. Every once in a while, the computer will do this, but instead of just blacking out, there will be a blinking white box which I believe to be my cursor or a line position indicator.
Also, when I play games that open in their own window on my screen and this happens, the game minimizes and I'm looking at my desktop. One game I used to play, it would minimize and show me the desktop sometimes and other times it would disconnect me from the game's server.

I have checked my power settings and put them all to off/always on accordingly and that doesn't seem to do anything to help the situation.

Any help will be greatly appreciated.
*I would also like to throw in that I know my way around the basics of a computer, but nothing technical. Please try to keep the descriptions and help simplified for me.*

Ok, simple... Lets start with what is this computer? Laptop, desktop, XP, Vista. Make, model? Monitor, LCD, CRT?