Just started the Prophet quest on the Dawnguard side, but whenever I talk to Serana, she says "If you want me to come with, it has to be just you and me" and nothing else? I've no other followers, so why does she refuse to even talk to me?

Alright, the game seems to think I have a follower in my service when I don't. Anything command that forces all my followers to leave. Or alternatively, any quest.

Try console:
set playerfollowercount to 0

Excellent, that works!