I just recently figured out that template tags such as edit_post_link - tags that show certain things when you are logged in - only show under certain parameters.
1. You must be using permalinks for your blog.
2. You must use the correct address for the "Edit" or "Logged in as.." to show. It must match the URL in some form that you put in your General Options. This means that if you put http://yourdomain.com, if you use http://www.yourdomain.com to view your site, the links won't show. You must use http://yourdomain.com, without the www
This has been the case with an old 1.5 blog that I update, as well as two 2.0.2 blogs.