I had this question on my old blog from time to time (http://www.elizabethingersoll.blogspot.com/), and I'm already having it again. I'm not 100% sure, but I hope this is the right answer. It doesn't seem to affect everyone the same way.
I logged out of Blogger and tried to leave a comment like an anonymous user.
I installed a new CommentLuv portion to my template, so that may have changed things. You can try to click "Links to this post" and, for me anyway, that opens them up.
The old way, before I tinkered with my template, worked like this:
Beneath each post, it should say "0 comments." Well, at least it does right now - I hope that changes soon though :-) If you click on "0 comments," the window will open that will let you leave a comment of your own.
I think that's the answer. If you try to leave a comment that way, or any way for that matter, and it doesn't work, will you try to email me and let me know so I can investigate it more? I'm email@example.com. I'd appreciate it very much. Thanks for helping me improve my blog!