wp_nav_menu() doesn’t work

You might need to use ‘add_theme_support’ for ‘nav-menus’ as well. See line 2 below:

if ( function_exists('wp_nav_menu') ) {
  add_theme_support( 'nav-menus' );
  register_nav_menus( array( 
      'primary' => __( 'Main Menu', 'wsy' ), 
      'secondary' => __( 'Secondary Menu', 'wsy' )
      ) 
  );
}

Then display your menu like so:

$nav_menu = 'primary';
if ( has_nav_menu( $nav_menu ) ) {
echo '<nav role="navigation">';
  wp_nav_menu(
    array(
        'theme_location' => $nav_menu,
        'depth' => 1
    )
  );
echo '</nav>';
}