Throughout the movie, Ray tries to drown out the voice he hears the only way he knows how: playing his guitar as loudly as possible. In his house, then once again in the motel, he is stopped from doing so. Eventually, he has nowhere to go and no way to fight the influence, short of killing himself.
The act of him giving his guitar to Zooey can be seen as giving her a mean to protect herself and her family.
The Devil wants Zooey, but Ray feels sorry for her, and tries to appease Him by giving Him another child.
Eventually, Ray succumbs to the influence. However, he also intends to kill himself. Instead of the usual M.O. of dismembering and burying the victim, he prepares to burn alive Zooey and himself as well. When Jesse climbs into the room, Ray eventually manages to control himself and willingly lets Jesse kill him, knowing he will be freed.
It could be seen that it was God that was telling Ray to kill, and Satan was telling Jess about Ray's crimes through inspiration for his art. Note, the focus of the opening is Ray trying to drown out the voice in front of an upright crucifix, while the start of Jess' involvement is implied to be when he's inspired to paint the inverted crucifix. Ray thought Satan was telling him to kill because he was brought up Catholic, and that would be the obvious case in that religion's worldview (Biblical precedent for Godly directives to commit infanticide notwithstanding)
Genius Bonus: Leonard, the name of the museum curator that Jesse meets with, is also the name of a demon from the Dictionnaire Infernal. Seeing how Jesse sees a goat with four horns after meeting him (although the image of Leonard in the Dictionnaire has three), this connection is likely intentional.
Moral Event Horizon: Eventually, Ray stops trying to drown out the demonic voices in his head, and returns to murdering children. It's at this point that the viewer might stop feeling sorry for him and start seeing him for the revolting child killer that he is.
