Re: cannot re-login to a new install
Since this may involve sessions, one thing to try is turning off or on "Store session data in database" on the Admin General page (tiki-admin.php?page=general) and seeing if there is any change. I have no idea if this is relevant, though. I'm not sure what you mean when you say the sessions table was goofed up. Do you mean it needed to be repaired? Generally there is a specific error message when this happens.
In my experience sometimes two Tiki sites running on one server can have problems since the cookies are set according to domain. You can set the "Remember me path" for each, if they share a domain, and this might reduce any cookie confusion (I believe the path is the Apache environment document root, as indicated on tiki-phpinfo.php).
I've also seen the "Cookies must be enabled" message a few times with Tiki and know that feeling of being falsely accused. I can't recall now what the problem was but it was fairly shortlived, I think something like deleting browser cookie info for the site might have been involved. Also, have you tried different browsers and if so is the behavior consistent? Browsers seem to vary quite a bit in how they handle cookies.
-- Gary