Most monitors (screens) will turn off if they do not get a signal from the computer. When you turn the monitor on, the power light will turn to green as the screen is looking for a signal. When it does not find a signal, the power light will turn to yellow or turn off. If it does eventually get a signal, the monitor will come back on.
So the first thing I would suggest is that you check the cable between the computer and the monitor. If that seems to be OK, I would suggest finding a different monitor and hooking it up to your computer. If it works, your other monitor is going bad. If it does not work, something is wrong with the computer.