As long as you did not delete the wordpress database, the Atahualpa options should still be in the wp-options table.
When you deleted the Atahualpa folder from the 'themes' folder, if you went into your site, you should have seen the default theme. What you had done is removed the cod that process the Atahualpa options.
When you reload the Atahualpa folder in the 'themes' folder, and activate it, it should pick up all the existing theme options. This is why you can have two (or more) versions of the theme in different folders in the 'themes' folder and swap back and forth. (caveat -newer releases of the theme may introduct options that don't exist in the older versions and things will change - like 34 can have 4 sidebars where as earlier versions only had 2)
If you deleted your Wordpress database you will need to restore a backup because you will have lost ALL your data.
You can verify that your Atahualpa settings exist by going into phpMyAdmin, selecting your database and issuing this SQL statement
SELECT * FROM wp_options WHERE option_name REGEXP '^bfa_ata_'
make sure the prefix for the options table matches what you set in wp-config.php