Well, I see you posted some more info while I was composing this very long response. It looks like you are getting back on track. Anyway, here are my recommendations. Sorry for the length.
It sounds like you have a temporary folder called store_new. So I take it you have not upgraded your live website yet, but are putting together a v1.3.8 separately, right?
You can do that, and you can view it online, but it complicates things a bit in helping your sort out this issue.
I am going to assume your live site is at http://aphrodisia.com.au/shop/.
I'm also assuming that your v.1.3.8 has been placed at http://aphrodisia.com.au/store_new/shop/
The only entries you needed to check and change were:
define('DIR_WS_CATALOG', '/');
define('DIR_WS_HTTPS_CATALOG', '/');
Your change to:
define('DIR_FS_CATALOG', '/hsphere/local/home/houseofd/aphrodisia.com.au/store_new/shop/'); looks okay.
Based on the above, I "think" define('DIR_WS_CATALOG.... etc. should read:
define('DIR_WS_CATALOG', 'store_new/shop/');
Likewise, define('DIR_WS_HTTPS_CATALOG'..... should read
define('DIR_WS_HTTPS_CATALOG', 'store_new/shop/');
all the others should have been left in their default settings.
Reset the following back to this:
define('DIR_WS_IMAGES', 'images/');
define('DIR_WS_INCLUDES', 'includes/');
define('DIR_WS_FUNCTIONS', DIR_WS_INCLUDES . 'functions/');
define('DIR_WS_CLASSES', DIR_WS_INCLUDES . 'classes/');
define('DIR_WS_MODULES', DIR_WS_INCLUDES . 'modules/');
define('DIR_WS_LANGUAGES', DIR_WS_INCLUDES . 'languages/');
define('DIR_WS_DOWNLOAD_PUBLIC', DIR_WS_CATALOG . 'pub/');
define('DIR_WS_TEMPLATES', DIR_WS_INCLUDES . 'templates/');
define('DIR_FS_DOWNLOAD', DIR_FS_CATALOG . 'download/');
define('DIR_FS_DOWNLOAD_PUBLIC', DIR_FS_CATALOG . 'pub/');
define('DIR_WS_UPLOADS', DIR_WS_IMAGES . 'uploads/');
define('DIR_FS_UPLOADS', DIR_FS_CATALOG . DIR_WS_UPLOADS);
define('DIR_FS_EMAIL_TEMPLATES', DIR_FS_CATALOG . 'email/');
Note, if my assumptions about you setting up v1.3.8 as a separate test site are correct, then when you move the files up to /shop to update your live website you are going to have to change
define('DIR_WS_CATALOG', 'store_new/shop/');
to
define('DIR_WS_CATALOG', 'shop/');
and change
define('DIR_WS_HTTPS_CATALOG', 'store_new/shop/');
define('DIR_WS_HTTPS_CATALOG', 'shop/');
Similar changes need to be applied to admin/configure.php.
In the future, unless you are doing some extensive revamping of your website at the same time you upgrade, I recommend that you simply run the upgrade script to install over your current website files. Each ZenCart upgrade is very throroughly vetted before being posted and you should enounter no problems upgrading unless you have made modifications to the core files or have modified default_template files instead of using the template override method.
If you have modified the default_template files, now is the time to brush up on the template override system and start using that method. It will make future upgrading much easier.
Don't take this a being critical of your methods. I've done exactly the same thing myself, but have resolved not to do it that way again. Sometimes we can be overly cautious. In my opinion, the better way to assure I don't crash my website during an upgrade is to simply make a backup of the site just before upgrading. If the new install crashes, I can always restore using the backup and then go figure what happened and try again later.
Ron