Have you edited the config.php with your database login information? If you get that error, it means the credentials are wrong and it actually can't connect, so double-check them.
Also, if you changed the paths in functions.php at the top, you can make it just "zenphoto" again and it should work as long as it matches the actual folder name. (You did change the paths, didn't you? It's the only way for the 1st error to occur...)