$mech->submit_form(   # invoke the submit_form() object method.
  $form_string => $d, # Anything to the left of a 
                      # => is treated as like it's 'single quoted'
                      # That means variables are not interpolated.
                      # This is a possible bug in your script,
                      # but not the one you're asking about.
                      # *** Next comes the bug you're asking about.
  fields => {         # The curly bracket begins an
                      # anonymous hash.
    $param_string     # This is a single scalar value
  }   # You've completed the creation of the anonymous hash, but
      # you created it with one key (the contents of $param_string)
      # and no associated value.  So you get an error message.
);

##</code><code>##

$mech->submit_form(
  $form_string, $d,
  fields => { 
    split( /=>\s+|,\s+/, $param_string ) 
  }
);