You have a multipart message. You need to go through the parts and find the one that is a mime_type text/html or text/plain Try the following code.

 if ($MIME_entity->parts > 0)
{
   for (my $i=0;$i<$MIME_entity->parts;$i++)
   {
      my $subEntity = $MIME_entity->parts($i);
      if (($types->{$subEntity->mime_type} eq 'text/html')
           ||
           ($types->{$subEntity->mime_type} eq 'text/plain'))
      {
         if (my $io = $entity->open("r"))
         {
            while (defined($_=$io->getline))
            {$recHash->{body} = $recHash->{body} . $_;}
            $io->close;
         }
   
      }
   }
}
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UPDATED, the following code works better

#!/usr/bin/perl

use MIME::Parser;
use Data::Dumper;
$parser = new MIME::Parser;
$parser->ignore_errors(1);
$parser->output_to_core(1);
my $MIME_entity = $parser->parse(\*STDIN);
my $error = ($@ || $parser->last_error);

if ($MIME_entity->parts > 0) # Is this a multipart
{
   print ">> Multi Part Message\n";
  for (my $i=0;$i<$MIME_entity->parts;$i++)
  {
    my $subEntity = $MIME_entity->parts($i);
      print ">> MIME: ", $subEntity->mime_type," \n";
    if (($subEntity->mime_type eq 'text/html')
          ||
        ($subEntity->mime_type eq 'text/plain'))
    {
       if (my $io = $subEntity->open("r"))
       {
           while (defined($_=$io->getline))
              {print $_}
           $io->close;
        }

     }
  }
}
else
{
   my $body = join "",  @{$MIME_entity->body};
   print ">> Not a multipart\n";
   print $body;
}
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