mod_perl isn't necessary to run Perl CGI scripts in Apache. (But it may speed up some of them.)
What may be missing but isn't clear due to the rather incomplete configuration shown above, is, if mod_cgid or mod_cgi are loaded. In Apache 2.2, it depends on the MPM which of those two you have to use.
If you're on Debian or Ubuntu, calling a2enmod cgi
or a2enmod cgid
plus a service apache2 restart
may already suffice to solve your issue. Not sure if these helper scripts are available on other distributions, too.