Do you get focus confirmation when focusing manually? I presume not.
It seems like that if you really want AF there is no choice but to have the camera serviced. To the best of my knowledge there is very little you can do yourself as all parts involved are delicate and precision calibrated. Even if you spot some dirt on the mirror, for example, it will be difficult to remove without scratching the mirror.
You could try to go into the
debug menu and see if the AF adjustment has some crazy value (it normally is "0"), but I'm really clutching for straws for you here.
Good luck, its such a nice camera.