There does seem to be a problem in your files.... I got the error:
You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'ANDProductID IN (SELECT ProductID FROM ps3_productcategories AND(CategoryID = 15' at line 1
which implies that somewhere there is text " AND" which should be " AND "... so it is missing a space. This appears to be the cause of the issue... most likely it is on the ProductLookup.php page, which is the page used with AJAX to load the category search results and the issue is probably repeated on the ProductsResults.php page as well.
I'll open a support incident so that we can work with you directly to find where the error occurs and add the missing space character, which appears to be the source of your problem.
