Ah, but you really do have one PM... the sender profile is probably screwy. FTP into Members/pm_users, and grab the file with your user number. Inside, you'll see a reference to a PM topic in the form of X-00000007, where X is the directory in Members/pm_topics, and 7 would be the PM topic number.
You can open that file up to determine who the sender is so you can determine if the profile is b0rked or not.
As for the cookie mess... having it work when not logged out makes quite a bit of sense, as the error only occurs when profiles are being authenticated. %)
Upgrading to 6.6 will remove all of your hacks, which may help with the problem.