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It sounds like the cinema display is not showing the same image that the Macbook.
If by that you mean it shows the desktop wallpaper, bit does not mirror the computers monitor, then take a look at this article.
How to use multiple displays with your Mac
If there is no video at all from the computer to the display, then I suggest the troubleshooting outlined in this article named Apple computers: Troubleshooting issues with video on internal or external displays found here http://support.apple.com/kb/ht1573.
All the best,