Unfortunately a lot of the support people you get in touch with don't understand what is going on. If you give them more information than they need, like telling them you are using a third party shopping cart, it makes it too easy for them to pass the buck.
Just create a new blank page with this code:
$_SESSION['savetest'] = "working";
Then create a new blank page with this code:
Visit the first page and then go to the second page. It should show the session variable "savetest" has the value "working".
It it doesn't, show that to GoDaddy and they won't be able to pass the buck because the code is so simple you can see that the session variables aren't being set properly. You probably just got a bad support person.