FBLike does not work even without enabling XFBML

I am setting up multiple sites with a single WP installation. I did a network activate, and I see the Like buttons on all the sites and all the posts. But, when I click it, it says “<Name> likes this article”, and after a second goes back to “Be the first to like this among your friends”. Nothing that I “liked”, is linked back my fb profile, so basically, the plugin is not working.