It looks like your search is setup to work with the posted values:
//comparison list additions
$WADbSearch1->addComparison("ARTIST_idARTIST","".((isset($_PO ST["S_ARTIST_idARTIST"]))?$_POST["S_ARTIST_idARTIST"]:"") ."","AND","=",1);
$WADbSearch1->addComparison("idCATEGORY","".((isset($_POST["S_idCATEGORY"]))?$_POST["S_idCATEGORY"]:"") ."","AND","=",1);
You can fix this one of two ways. You can either update the search forms method to be get instead of post, and update the code to work with the get like this:
//comparison list additions
$WADbSearch1->addComparison("ARTIST_idARTIST","".((isset($_GET["S_ARTIST_idARTIST"]))?$_GET["S_ARTIST_idARTIST"]:"") ."","AND","=",1);
$WADbSearch1->addComparison("idCATEGORY","".((isset($_GET["S_idCATEGORY"]))?$_GET["S_idCATEGORY"]:"") ."","AND","=",1);
The other way you could update this would be to use the request instead of post or get, this will work for either a posted value or one that comes through the url. It should look like this:
//comparison list additions
$WADbSearch1->addComparison("ARTIST_idARTIST","".((isset($_REQUEST["S_ARTIST_idARTIST"]))?$_REQUEST["S_ARTIST_idARTIST"]:"") ."","AND","=",1);
$WADbSearch1->addComparison("idCATEGORY","".((isset($_REQUEST["S_idCATEGORY"]))?$_REQUEST["S_idCATEGORY"]:"") ."","AND","=",1);