Cool music, awesome art! I really wondered what was going on here. It reminded me a little bit of Donnie Darko.
The controls in the platforming section are smooth enough, but it is annoying how you die with one hit, especially since it takes several seconds for the game over to take effect. I think it would have been okay to be a bit more generous and give the player 3 hit points. Also, the attack doesn't strike very far, so you have to time your strikes just right. This takes a bit of getting used to.