Why does this search.php not work?

I see at least two potential issues:

1. You have if ( have_posts() ) : twice.

Here:

<?php if ( have_posts() ) : ?>
<h1 class="page-title"><?php printf( __( 'Search Results for: %s', 'nothing' ), '' . get_search_query() . '' ); ?></h1>

And here:

<ul id="post-list">
<?php if (have_posts()) : while (have_posts()) : the_post(); ?>

1. The get_template_part() template tag expects a filename slug, rather than a path. So you may want to use the locate_template() template tag instead for these:

Try:

<?php  locate_template( 'includes/inc-image.php' ); ?>
<?php  locate_template( 'includes/inc-detail.php' ); ?>

EDIT

The locate_template doesn’t load any content when i apply that…

Do those files exist?

…and removing one of the if gives me an unexpected T_ELSEIF error… 🙁

Yeah, because you have an improperly opened/closed else/if construct. Get rid of the stray endif here:

<?php  get_template_part( 'includes/inc-image' ); ?>
<?php endif; ?>

EDIT 2

So, here’s a rewrite, attempted to fix your syntax errors:

<?php get_header(); ?>

<h1 class="page-title"><?php printf( __( 'Search Results for: %s', 'nothing' ), '' . get_search_query() . '' ); ?></h1>

<?php if ( have_posts() ) : ?>

    <ul id="post-list">

        <?php while (have_posts()) : the_post(); ?>

            <?php
            $featured = get_post_meta($post->ID,'_thumbnail_id',true);
            $attachments = get_children( 'post_type=attachment&orderby=menu_order&exclude=".$featured."&post_mime_type=image&post_parent=".$post->ID );
            $vimeo = get_post_meta($post->ID, "rw_post-vimeo',true);
            ?>
            <li class="post">

                <span class="entry-published">
                <time datetime="<?php the_time('Y-m-d')?>"><?php the_time('F jS, Y') ?></time>
                <!--Start Single Image-->
                <?php  get_template_part( 'includes/inc-image' ); ?>
                <!--End Single Image-->

                <!--Start Rest Of Post Content-->
                <?php  get_template_part( 'includes/inc-detail' ); ?>

                <!--End Rest Of Post Content-->

            </li>

        <?php endwhile; ?>

    </ul>

    <section id="pagination">
    <?php wp_pagenavi(); ?> 
    </section>

<?php else : ?>

    <h2><?php _e( 'Nothing Found', 'nothing' ); ?></h2>
    <p><?php _e( 'Sorry, but nothing matched your search criteria. Please try again with some different keywords.', 'twentyten' ); ?></p>
    <?php get_search_form(); ?>

<?php endif; ?>

<?php get_footer(); ?>

Verify that works, and then we’ll tackle the template-part output issues.