You should use a dual-link DVI to Mini DisplayPort adapter to connect your LED Cinema Display (27-inch) to a computer that has a DVI video port. Using an adapter that supports only single link connections may generate a "no video" condition, may result in poor image quality due to the lack of native resolution support, or the LED Cinema Display's native resolution of 2560 x 1440 may not appear in the Display preferences. Other compatibility issues may also occur.
If you are using your LED Cinema Display (27-inch) with a DVI video card and experience a "no video" condition, check the following:
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- Locate the make and model of the DVI to Mini DisplayPort adapter and refer to the manufacturer's website to confirm that the adapter has dual-link DVI support and works with the 27-inch LED Cinema Display. Some adapters support only the LED Cinema Display (24-inch, Late 2008). 

- Verify that the display's power cord is firmly connected and plugged in to a known good outlet. 

- Make sure all of the display and adapter cable connections are secure. 

- Confirm that the computer is running Mac OS X v10.6.4 or later and that all available software updates have been installed. 

Learn more
For additional troubleshooting, refer to Apple Computers: Troubleshooting issues with video on internal or external displays.