Q: I have an old 30 inch Cinema Display that the power cable that plugs into the brick broke. Is there a way to get the cable replaced?

You might try taking it, the cable that is, to an Apple store genius bar and see what they say...if they will sell just that piece to you.  Should not be very expensive.

Hauling a 30" display to a store isn't going to be much fun, especially if they cannot fix it.  Try calling Apple support, http://support.apple.com/kb/HE57 and see what they suggest.  If they say the Apple store can take care of the display for you, at least you know there is a good reason to carry it in.