Take the battery, and card out for about 15 minutes. Replace, and see. If this gets it on, re-set to factory default in the menu.
I doubt this will help probably some heavy dust, or small piece of grit in lens mechanism. Sometimes tapping around on the camera body near the lens will dislodge the grit, do this with your finger smartly. Not a hammer.
I don't think you will want Canon to repair this, it would be just as cheap to buy another one. They will not accept a manufacturing fault, this is only about the second time I have seen this complaint on the G12.