Just found and solved the same problem.
Found your thread and it gives me a clue that widget did work which i did not notice. 🙂
so I compare code of widget and the menu bar search function.
Solution: edit the header.php
found this line:
<form id=”searchform” method=”get”
action=”/”>
change it to:
<form role=”search” id=”searchform” method=”get”
class=”searchform” action=”http://Your.domain.com/wordpress-path/”>
Done.
Have a nice day.
