Did you do the "take the battery out, keep it out for, say 24hrs, put it back in" routine? If you didn't, do that first with a fresh battery. If that doesn't work, yeah, it sounds like a repair job. I don't have an idea how much that is gonna cost - it might be dependent on where you are in the world. Why not ask Sony for an estimate?
Das Bild ist ein Modell der Wirklichkeit - Wittgenstein