I'd just keep a session variable that says whether they're logged in or not logged in (plus other session variables as needed, but they don't play a role in this).
Initially (on the home page) it's set to "not logged in", then if and when they decide to log in, it's updated to "logged in".
On each page, you just need to check the value of this variable to decide what information to display.
You could have a wee login form on every page so's users can log in any time they want. Using $HTTP_REFERER or a hidden form field in the login form to identify which page was being displayed at the time, the login script could check them off against the database; set the login session variable to "logged in" if it's a valid login, then redirect the browser back to the page the login was made from.
From the user's point of view, an invalid login would have no effect beyond a page refresh, while a successful login would refresh the page with the new information.