It may not be something that needs a repair!
A lot of people run in to this same issue and most of the time it can be fixed by a specific order of powering the devices.
First off go ahead and power down the Macbook pro.
Now make sure that the cinema display is plugged into the Macbook pro, all three cables.
USB, Mini display, and a power cable.
Now boot the Macbook Pro, and if all is okay with the monitor it should power on at this point with the Macbook pro.
Let me know if this helped!