If there is visible damage on the lens then there has likely been a physical blow to the lens that may have forced it back. These lenses are made with plastic gears for zoom and focus and they break easily. The first part of the power up cycle is to check the lens and if it gets no reaction then you won't be able to power on.
Unfortunately (or fortunately depending on your view) the camera prices are coming down so fast that most repairs aren't worth the investment as they start generally at $100 and go up from there. Since this is at least a four year old model the equivalent replacement is likely considerably cheaper and better than your current model.
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