If you are redirecting you need to do $q->redirect("form.cgi?key1=val1&key2=val2");
You also combine them into 1 script and do something like this

if(defined $q->param('form_submitted')){
  if(&errors){ #Error occured
    &display_form($q);
  }else{
    &thank_you;
  }
}else{
  &display_form;
}

sub display_form(){
  ##Do form stuff
}
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Also in display_form(), you might want to consider using HTML::Template and doing

$temp = HTML::Template->new(
                      file => 'file.tmpl',
                      associate => $q
              );
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which will put all the submitted values into the template as long as the associated <TMPL_VAR NAME=".."> tags are there.