I purchased a "Mini Display Port to Dual-Link DVI Adapter" for $99 dollars from the Apple Store and it solved the problem. The Monoprice 27" Crystal Pro IPSLED display has too high of a resolution for just a standard DVI connector.
The following Apple support link has this information: http://support.apple.com/kb/HT3382#11
This explains that monitors with higher resolutions than 1920 x 1200 must use this adapter. It requires both the DVI and the USB to be connected.