PDOException when creating the table: Base table or view not found
I had the same problem, and in my case the issue was the database tables engine: By default it is InnoDB and (for some reasons I still don't have to understand) Drupal reports this error.

You must change the database engine to MyISAM. First off, you must be sure the tables that are going to be created by Drupal have MyISAM as engine: In /includes/database/mysql/schema.inc, look for createTableSql($name, $table), and change InnoDB to MyISAM; then, save it.
Since you have a few tables in your database they must be changed to MyISAM as well, so simply export the database as .sql file open it in a text editor and replace Engine=InnoDB with Engine=MyISAM. Now in the server phpmyadmin delete all the tables of the DB and import the new .sql file in there. In this way, all your tables and the tables that will be created by Drupal are MyISAM.