Error in documentation
You said "It looks like your login link is actually going to your logout page. On this page is a check to see if the user is logged in, if they are not they are taken to the login page. The problem is that the login page will try to take the user back to the logout page on a successful login."
This is because there is an error in your step-by-step documentation. If you look in the file "Incorporating the user registration solution pack into your existing site.pdf," you will find the following:
"Log In: A link on all public pages is often appropriate beside the Register link. Simply create a link to the users_LogOut.php.
When a registered user accesses the users_LogOut.php page, they will automatically be logged out of the system."
This is clearly an error that tripped me up until I read it carefully. There is a whole paragraph missing. The Log In paragraph should finish with linking to the users_LogIn.php file, and then there should be a Log Out paragraph.
I too am a new user and I find this type of support documentation very disturbing. I can't get my stuff to work either and some of this is due to unclear step-by-step instructions.