After turning off the monitor, can not be turned

We need a little more information. After you turn it off, is the computer off, also? If you turn on the monitor (does it have a yellow or green light), and then turn on the computer, do you see anything on the monitor.
Is the monitor plugged into the wall and is the power cord tightly plugged into the back of the monitor (sometimes comes loose).
If the monitor will not turn on at all after you've checked the above things, then it has gone bad on you.
If you get a light on it and you have turned on the computer but there is no display, it is very possibly the video card.
Of course, this all assumes that the computer is actually starting up.