I understand that the song played at the end of True Blood (Season 3, Episode 4 - 9 Crimes) is called 9 Crimes by Damien Rice [I knew the song before it was in the episode]. I would like to locate that VERSION played at the end, for I can't find it.

From what I gather, it was the Demo version of the song, still by Damien Rice. You can find it on itunes. Its the last song on the list:

link

ALSO, someone pointed out that the song clip used by the show was cleaned up/edited by production. So its still a bit different, and you wont find it online, since it was specifically for the show.