I take it from your description that the game plays blind (that is, you can coin it up and get game play sounds, but you get no display). If so, it sounds like a component on your monitor has failed causing it to be unable to start.
If you want to fix this yourself, the place to start is by identifying the type of monitor (there's a stickied post in this forum with hints on how to do that - be sure to read it). You will need to be comfortable with soldering components on the circuit board of your monitor to fix this and be aware of a few safety issues. The actual component replacement isn't usually too hard, and the parts themselves are usually only a few bucks, but the troubleshooting can take a while, especially if you have very little experience.
If you don't feel comfortable doing that, I'd suggest hiring somebody to fix the monitor for you.