Don’t know why this is happening, as we did use a licensed media to install. The product ID is embeded in the media and no need to manually input. Anyway, I ran the SQL server installation media again, and chose Maintenance -> Edition Upgrade, then just followed the wizard without changing anything as I saw the product ID is there. After that, the issue went away. We were able to use the SQL server management studio again. This could be a bug according to this Microsoft KB. It is not exactly the same as my scenario, but should be relavent.
We ran into the problem this morning – an error Window poped up saying the evaluation period has expired when I launched the SQL Server Management Studio.