If your page has a HTML form with a submit button and uses the POST method you can solve your problem very simply. Here is an example from the lwpcook manpage:

use HTTP::Request::Common qw(POST);
use LWP::UserAgent;
$ua = new LWP::UserAgent;

my $req = POST 'http://www.perl.com/cgi-bin/BugGlimpse',
              [ search => 'www', errors => 0 ];

print $ua->request($req)->as_string;
[download]

All you have to do is set up a POST request message with all the fields in your HTML form (check boxes, text fields, and so on), with the correct URL. I hope this helps.
marcos