Start out with a more simple test and work up from there.

Your problems could be coming from anywhere (even an incompatibility between the version of the DBI module and your mod_perl).

So start with a handler like this:

package My::Simple;

use strict;
use warnings 'all';
use Apache2::RequestRec ();

sub handler : method {
  my ($class, $r) = @_;

  print "content-type: text/html\n\n";
  print "<h1>HELLO WORLD!</h1>";
  return 0;
}

1;# return true:
[download]

And in your httpd.conf add the following:

<Perl>
  use lib '/path/to/your/libs';
</Perl>

PerlModule My::Simple

<VirtualHost *:80>
  ServerName www.your-website.com
  ServerAlias your-website.com

  SetHandler perl-script
  PerlResponseHandler My::Simple
</VirtualHost>
[download]

Restart your Apache httpd server and access yoursite.com/.

In your browser, you should see...

HELLO, WORLD!

...and your logs should not contain any errors.

Once you have confirmed that Perl, Apache and mod_perl are working, you can start debugging your own code, rather than expecting it to be an apache + modperl problem.