Comments enabled, but disabled at the same time

You can try the following function:

function enable_comments() {
    update_option( 'default_comment_status', 'open' );
}
add_action( 'after_setup_theme', 'enable_comments' );

This should enable comments for all new posts. On the other hand have you checked your theme? Some themes for some reasons have build in functions that overrides the default WP comments behavior.