I can't see Apache::Registry listed anywhere in your post. That will be why it can't find the request() method. Apache::Registry has details of adding this to your httpd.conf file.

Depending on your setup, you may need to add use Apache::Registry to login.cgi or some module it calls.

I usually like to keep my options open with something like:

use Apache::Registry;

my $r;

eval { $r = Apache->request };

if (defined $r)
{
    $r->content_type(...);
    ...
    $r->send_http_header;
}
else
{
    print "Content-Type: ... \n";
    ...
    print "\n";
}
[download]

That way your CGI script will work under both mod_cgi and mod_perl without modification.