I'm not sure what you're getting wrong - you seem to be getting most of it right.
Somehow your pages are being changed so that all of the links in your pages are being altered to be relative to your site root, and unless you are using another Application other than Dreamweaver (before using DW to upload them), then these changes can only have been made by dreamweaver itself. Is Dreamweaver the only application you are using?
If it is, then those changes can only have been made either by the way you have set up your site definition in Dreamweaver, or by the way you have set your WA_Globals; but these would only have been changed if you had been previewing and sending pages to a testing server, and then sending those to the server.
As the Power Store is a pretty much 'ready-to-go' application (apart from WA_Globals and localhost.php which you seem to have got down correctly) - all that need to happen once you have adjusted these two files, is to upload the entire site and it should be working as it should, 'out-of-the-box'.
What I suggest is to start with a clean copy of PowerStore, downloaded from your account 'Download' page. Before that, make a note of your connections/localhost.php details, and send the whole lot back up to your remote server (into your remote Host directory public_html/). This would put an untouched and known good installation on your remote site.
This needs to happen without testing anything out in Dreamweaver.
If this sounds like something you would be up for, and pending other suggestions, could you post back and we can take it forward a bit?