Mac OS X?
STOP, don't recopy anything yet...
I had this problem a couple of times on Mavericks. MySQL is no longer included, but my install is essentially the same as what you'd expect to find on Snow Leopard, I think, rather than MAMP or something.
After migrating from one computer to another I had this problem. It was the result of the MySQL control panel starting mysqld, rather than my starting it on the command line. (When migrating, this somewhat obsolete control panel forgets that you told it NOT to start on boot.)
Look at the processes (top or activity monitor), on my system: if owner is root, it was started by launched and doesn't work properly; the correct process will have _mysql as owner.
Sometimes, I have both process running side by side!
Oddly, you can do everything, including use mysql via command line. However, even though innodb tables are listed they generate a do not exist error on querying.
This seems to be an ownership issue, which may apply on other systems as well.