This should work:

my $data = [PROGRAM => $PROGRAM, etc...];
my $action = 'http://baygenomics.ucsf.edu/db/cgi-bin/blast/blast.cgi';
my $res = $ua->request(POST($action, $data));
if ($res->is_success) {
  print $res->content;
} else {
  print "Error: ", $res->status_line, "\n";
}
[download]

gav^