Hi Larry,
If the page is not being called by a menu item then the module will not be displayed unless the module is set to appear on all pages.
When I do things like this I use {loadposition mymodulename} and in the module I overtype the position with mymodulename and set it to appear on all pages.
As the position mymodulename doesn't exist in the template the module cannot be displayed unless the loadposition calls it within an article.
Looking at the links you provided, it appears that the login page is a basic page so my method would work. Alternatively you would need to identify the menu item where you have set the module to appear and then ensure that the link has that on the end.
For example...http://www.firewindandwater.com/index.php?option=com_content&view=article&id=69
is the demo link. If this was controlled from your hidden menu by item 269 then the link would need to look like this...http://www.firewindandwater.com/index.php?option=com_content&view=article&id=69&Itemid=269
Hope this helps