Sorry, forgot to mention that I also removed:

name   => "action",
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because all the buttons had that name.

#!/usr/bin/perl

use warnings;
use strict;
use WWW::Mechanize;   

my $mech = WWW::Mechanize->new();

my $tf_add = "http://rulai.cshl.edu/cgi-bin/SCPD/getgene2?ARG1";
$mech->get($tf_add); 

$mech->set_fields( 'start' => -450, 'end' => 50 ); # this part works

# but not this:

$mech->click_button( 
  value  => "Retrieve sequence"
);

#$mech->submit();

my $result = $mech->content();
print "$result\n";
[download]