OK, now you have it working, you have some options.
With display mirroring off, you are running an extended desktop with both monitors active. Your macbook display is still the main monitor and that is where the dock lives. You can move the dock over to the other monitor. Go to System Preferences>Displays.
But before you do that, if you have an external keyboard and mouse, you can turn the MacBook display off and put the MacBook out of the way with the cover closed. To do this, with the NEC monitor as well as your external keyboard and mouse connected, close the cover to put the mac to sleep. Now wake it by pressing a key on the keyboard. The mac wakes up, sees the cover is closed and that an external monitor is connected, and uses that monitor at full resolution as the main monitor.
See this apple tech note for more detail:
http://support.apple.com/kb/ht3131