In your wp-config.php file, look for this line:
$table_prefix = 'wp_';
What you need to do is make sure that the prefix that's there matches what it was on the old (existing) database tables, so if the prefix is db_ you'd have tables like db_posts, etc. If the prefix didn't match what was there origianlly then WordPress will install the new database tables, and not use the existing ones like you want it to.