This is pretty confusing... Your original install was using cPanel, now you using fantastico? Not really a good idea anymore, often changes the charset to a swedish latin charset when it needs to be a utf-8. Are you upgrading or creating a vanilla installation?
If upgrading, then do nothing to the database or moodledata folder. Using FTP, delete the Moodle code, but nothing else, everything except the config.php file. Copy an unzipped new code base into the Moodle server folder, and run it via your browser as is. This should open the Moodle and run through the upgrade process with a minimum of fuss.
phpMyAdmin can be use to manually upgrade a database, but it is not always successful. Can also be used to create a database and manage it, is an excellent tool, but not necessarily for what you might be trying to do.
Where are you installing to? A server? A linux desktop? What is the environment?
If you are installing to a desktop then why are you using all these fancy installation tools? A manual installation is just as valid as any other way.
If you are using a server, then first, make sure the server environment is stable. Check that the PHP version is the minimum required. Then using FTP upload the Moodle installation files to the root, and open the url, http://[your.ip.address.here]/moodle/install.php. Then you should just be able to standback and let it happen. You may need to use phpMyAdmin to create the database, but you do not need to edit it in anyway. Just make sure that the collation is a utf8_general_ci and the type is an InnoDB.