monitor will not come on

Did you disconnect and re-seat the video cable?

Do you have another monitor that you could try connecting to it? If that worked that would rule out any kind of graphics card failure. There is a very slim chance your cable could have gone bad, but more likely if the previously mentioned items do not work, then it could be a failure of the Cinema Display. Those things are 'tanks' though and I've not personally had one go south on me. You could try resetting the PRAM and unplugging the computer for a while, but I'm doubtful that would fix the problem.