You don't have quotes around the product name that's being sent to MySQL.
Code:
$query = "SELECT * FROM tbl_products WHERE product_name = '$search_product'";
You could also increase the functionality of the search by allowing the user to just enter a part of the product name using the following SQL :
Code:
$query = "SELECT * FROM tbl_products WHERE product_name like '%$search_product%'";
It wouldn't be a bad idea if you showed the SQL being executed when you get a fail ie :
Code:
$result = mysql_query($query) or die ("Search Query Fault : $query");
You could also add the error message as well.
EDIT : Sorry shammat - you must of posted while I was typing.