I had this problem with my Lenovo T420s. I would plug in the DisplayPort and nothing would happen, the monitor would just go to sleep.
It turns out you have to run the Nvidia control panel and enable the monitor from X Server Display Configuration. The name of the package, if you don't have it installed, is nvidia-settings.
If you have an ATI card, I don't know what works but I would assume there's some sort of ATI control panel.
UPDATE: this is no longer an issue in Precise Pangolin (Ubuntu 12.10). I upgraded this morning and DisplayPort is recognized the same way my VGA was.