This error generally means that one or more system tables cannot be found in the database.
This can occur if you've provided valid DB credentials in your configure.php files and the database itself exists but contains no tables. In this case you need to run zc_install to properly setup the database contents.
Further, this symptom most commonly occurs when moving your site to another server and not properly preserving the DB_PREFIX setting from the old site's configure.php into the new site's configure.php, thus the tablenames cannot be located because they don't match up properly. Or you need to run zc_install to create the proper tables. Or you need to import the correct matching database data, since what you've got in the database presently isn't suitable for your current DB_PREFIX configuration.
(To manually figure out the correct prefix to use, look at the database using phpMyAdmin and see what common 2-4 letter prefix starts all the tablenames. Then set that value into the DB_PREFIX definition in your configure.php file.)