I chanced across this while searching for the same issue, that is I had exactly the same symptoms, USB and magsafe power worked, sound was coming out from the Cinema Display speakers, but there was no picture. I tried mirroring and other displays changes, but still no go.
I read the troubleshooting guides, and one of the suggestions was to reset the power manager on your computer, so I tried that. For a MacBook Pro what you do is shut down, then hold Control-Shift-Option-Power Button for a few seconds, and let. After that you power on as usual.
Those steps completely fixed the issue with the monitor.