Looks like the installation failed:
These two in the error log:
no fields found
'Table "config" does not exist'
So using whatever tool you have to view the contents of databases (phpmyadmin? or other), see if there is a mdl_config table in the moodle DB. Also check that the user you had to give the install form has access rights to create tables. Also, on the form concerning the DB variables during initial installation, there was one field that already had the prefix _mdl filled in. Did you change that?
There is a way to 'fix' via command line /admin/cli/install.php BUT your requirement is cPanel.
Not sure that php-intl is not required to install. It is, however, recommended:
http://docs.moodle.org/24/en/PHP_settings_by_Moodle_version
Looks like your easiest approach at this point is to re-install - from scratch.
However, maybe this might help:
There is more than one video on how 2 install Moodle via cPanel.
'spirit of sharing', Ken