...I'm really surprised that no one has said this yet (or maybe they have said it, just with more complicated words): if your character is apathetic and doesn't want to do anything, the obvious thing to do is put them in a situation where they are FORCED to do something.
Let's say they don't really care about having external goals, but they still care about being able to eat and sleep and stay alive-- disrupt that. Uproot them; force them to take a new job in order to survive; force them to live with someone that has different ideals. Push them into a more active role where they have to do things to maintain the world around them, even if they don't want to.
Or if even being alive doesn't concern them anymore, there's always the supernatural. ^^ Maybe they decide to die, only to find out that there's an afterlife to contend with that's not so easy to escape. Maybe some magical force hijacks their body and makes them do things against their will. Maybe the world goes through a paradigm shift, and all of a sudden there are new things in existence that they CAN care about.
Whatever you decide to do, once they're in that new situation, that's when you can give the protagonist opportunities to grow and change, and use those opportunities to gradually take them from their old mindset to their new mindset. Like, you know...storytelling. ^^;
It doesn't matter if your protagonist starts out with no goals; they're not the ones in charge of the story. You are. If they don't want things to move forward; YOU move them forward and make them deal with it. I mean, sure, characters should have influence over the kind of story they're in, but only up to a point. At the end of the day, it's the author's job to get them to where they need to be.