simple wordpress ajax plugin not working when not logged in

You want to use wp_ajax_nopriv_ for handling ajax for non-authenticated users:

// logged-out users
add_action( 'wp_ajax_nopriv_my_action_search_key_press', 'action_search_key_press_callback' );

// authenticated users
add_action( 'wp_ajax_my_action_search_key_press', 'action_search_key_press_callback' );