keesiemeijer on "search.php is not working at all"

Try showing the search form with get_search_form(): http://codex.wordpress.org/Function_Reference/get_search_form

Or try naming the name attribute "s".

<form method="get" id="searchform" action="<?php echo home_url( '/' ); ?>">
 <div>
    <input class="text" name="s" size="32" maxlength="64" />
 </div>
 </form>