Maybe she is intimidated by you.
Does she avert her eyes when she talks to you? Does she seem to have problems making eye contact, and/or look away when you look at her?
I used to be really shy, and sometimes when I liked a guy, I would get like this. Because I was infatuated, I would get all "omg he is amazing, he would never like me, he is so much better than me". I would get very self-concious and feel like I had to be impressive if I said anything...if we had little in common, it would be worse, because I would feel like an idiot when he talked about things he was interested in (as I could say nothing about it)...
So yeah, maybe she does like you, but is intimidated.
Even if she does, though, I doubt a relationship would work unless she could start to feel more comfortable around you.
Oh, and sometimes, I would be normal at first, but if I knew the guy knew I liked him, that's when I would get quiet, as I felt embarrassed that he knew.