I presume you mean a 23″ (not 24″) Apple Cinema Display?
If so, be aware that the Power Supply Units for different size Cinema Displays are not interchangeable.
A 23″ unit ships with a 90W PSU, a 20″ only with a 65W PSU.
A 90W PSU will work with both 23″ and 20″ Cinema Displays, but a 65W PSU will only work with a 20″ Cinema Display.
I guess this will only help if you have a mixture of 20″ and 23″ CDs, and have been swapping them around. Both PSUs look nearly identical, which doesn’t help. The Wattage is however written on the PSU somewhere.
Only a thought…