"Und was musste ich jetzt hören?"
I'm not sure, but it seems to me that "now" and past tense are incompatible in English.
I'm with you on that. FWIW my German wife also struggled with how to translate it. I think our best guess is that this was someone who was talking to herself while trying to remember her to-do list her music teacher gave her: "Now, and what did I have to listen to?" or a father is on the computer and his child says "listen to me sing this song" and he says "one minute" finishes his task and then says "Now, and what did I have to listen to?"
Good examples. The sentence does work in the right context but I think it is a little poorly worded.
any way - what do i have to hear now? - make more sense than any other germanic speculation :)