thats odd, im using basically the same code (http://zbdesign.biz/code/search.php -> view source)
its a somewhat messy method, but it works pretty good. i bet its something stupid that were both missing
actually i found something, you define $searchterm, but in the query its $searchtermS -> also, try taking out the addslashes($searchterm). that might work
edit: if all that fails, put this in place of the mysql_query($query) ...
$result=mysql_query($query) or die(mysql_error());
b/c if its not returning rows, the query is fucked up