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My iTouch 16GB 1st gen was dropped and now power button cannot turn off power. Everything else works fine and it can charge up, but it eventually dies with no power off function.

there is a contact spring between the backplate and the logic board that is probably misalinged or broken. it is near the on/off switch and gold plated, you will recognize it as soon as you take off the backplate. extend that contact spring or resolder it, if it broke off and your on/off switch should work again.