Untested, but you can simplify that while loop and make it easier to read by switching to HTML::TokeParser::Simple:

while ( my $tag = $tp->get_token ) {
  next unless
    $tag->is_start_tag($s_tag) 
      and 
    ($tag->get_attr($s_attrb) || '') eq $s_value
      and
    ++$start;
  last if $tag->is_end_tag($e_tag);
   
  if ($tag->is_start_tag('a') && $tag->get_attr('href')) {
      $data{$tag->get_attr('href')} = $tag->get_trimmed_text('/a');
      $count++;
      last if $count == $max;
  }
}
[download]

I may have missed some particulars, but you can see how the code is easier to read.