Moving Joomla to a different directory takes edits to the configuration.php file. There are a couple lines directing the site to the proper location from the server root that need to be adjusted. The database should still point to the proper place...IF YOU'RE ON THE SAME HOSTING ACCOUNT.
You'll want to clear all cache too.
There have been issues mentioned with sites running gantry that have moved and some items did not function properly. This was avoided by using the Akeeba Backup that others have mentioned above. It really is the best way to make a move and will save headaches in the long run.