Hi Gerry,
It looks something wrong with AND & OR conditions , I am not sure whether this works for you but,try
mysql_query("SELECT * FROM products WHERE prod_web='ja' AND (prod_naam LIKE '%$searchstring%' OR prod_k_omschr LIKE '%$searchstring%' OR prod_l_omschr LIKE '%$searchstring%')") or die (mysql_error());
Notice that i added braces