Menu block module overrides
Documentation for theme_menu_link():

function theme_menu_link(array $variables) {
  $element = $variables['element'];
  $sub_menu = '';

  if ($element['#below']) {
    $sub_menu = drupal_render($element['#below']);
  }
  $output = l($element['#title'], $element['#href'], $element['#localized_options']);
  return '&lt;li' . drupal_attributes($element['#attributes']) . '&gt;' . $output . $sub_menu . "&lt;/li&gt;\n";
}


The generated html needs to be returned as a return value.

The $variables argument has all the data.

Instead of var_dump(), you should install devel and do a dpm($variables). You might have to refresh the page twice to see the result.