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From my understanding of what you've previously posted, the login block is visible on your site and you've logged in using it, but it doesn't log you in, despite the fact it authorizes your login and confirms the authorization.
Hmm... the login and authorization should work with or without cookies, so that can't be it....
I was wondering if you can try something. On your website, visit user.php and see if you can login using that page.
If you are able to login using user.php, check your blocks and make sure the permissions are set correctly so that the "Login" block is only visible when it's an anonymous user and the "User Menu" is visible when it's a logged in user.
Try that and post back with the results.
-zimmi88 =)
P.S.: You can reach your administration page at admin.php.
"Need coffee, keep away..."