Why won't he die? I've taken down his health bar severall times, but he just wont die.

do you have the quest to kill him? otherwise he is essential.

see http://www.youtube.com/watch?v=_V45MVO45f0 in the end the Blades don't matter and can be ignored. I found that Paarthurnax will give a speech then fly away.

Yes I have the quest "paarthurnax"

My character's roleplay revolves around killing parthy

Because the gods are punishing you for trying to do so!

You've just gotta keep doing it. Eventually he will die. Try leaving and coming back. Or saving and reloading. I've had that problem too.