I think the net gives the right lyrics, but the meaning... I was thinking something along what you thought, but when I think about it "You don't mean nothing at all" can mean "you mean something to me", which would change a bit of the song's feeling.. Well, intentional or not, it makes the song really interesting, and if it's intentional, it would be even more, no?
What is your first language? Double negation is something I haven't really used to, as a non-native speaker of English.