After doing some research on your computer here is the best guess I can give. You indicate that the gateway has not been modified and you did not make changes to the software. The computer stopped responding and you turned off the power.
Based on that information, a cable or connection came loose inside the PC.That is a wild guess, but it is all I could find that meets the information you gave. Another possibility is the Video card failed. Or the card came out of its socket. I assume that this model came with a video card that has a PCI or AGP socket and is not on-board video. There is, I think, a cable that goes to the video card.
The fact that you here the sound indicates that everything else is working.
But in any case I do not recommend buying a new video car. Not yet. If you have a friend that collects old computer parts, ask him if he has an old video card. Try an old generic video card and see if it turns on the monitor.
EDIT: Forgot to mention. Some video cards fail to activate the monitor, you can 'fool' the monitor by turning it off and back on again. I heave an old PC that does this and that is how I deal with it. I refuse to buy a new graphics card.