WP_Query with “post_title LIKE ‘something%'”?

I need to do a WP_Query with a LIKE on the post_title.

I started with this regular WP_Query:

$wp_query = new WP_Query( 
    array (
        'post_type'        => 'wp_exposants',
        'posts_per_page'   => '1',
        'post_status'      => 'publish',
        'orderby'          => 'title', 
        'order'            => 'ASC',
        'paged'            => $paged
    )
); 

But what I actually want to do looks like this in SQL:

$query = "
        SELECT      *
        FROM        $wpdb->posts
        WHERE       $wpdb->posts.post_title LIKE '$param2%'
        AND         $wpdb->posts.post_type="wp_exposants"
        ORDER BY    $wpdb->posts.post_title
";
$wpdb->get_results($query);

The output prints the results i’m excpecting, but I use the regular <?php while ( $wp_query->have_posts() ) : $wp_query->the_post(); ?> to display the results.
And that is not working with $wpdb->get_results().

How can I achieve what I described here?

I would solve this with a filter on WP_Query. One that detects an extra query variable and uses that as the prefix of the title.

add_filter( 'posts_where', 'wpse18703_posts_where', 10, 2 );
function wpse18703_posts_where( $where, &$wp_query )
{
    global $wpdb;
    if ( $wpse18703_title = $wp_query->get( 'wpse18703_title' ) ) {
        $where .= ' AND ' . $wpdb->posts . '.post_title LIKE \'' . esc_sql( $wpdb->esc_like( $wpse18703_title ) ) . '%\'';
    }
    return $where;
}

This way you can still call WP_Query, you just pass the title as the wpse18703_title argument (or change the name to something shorter).