it's a second generation ipod touch
if the power button fails, it's in most cases a fluid damage or a worn out switch.
you can use the Power-Volume-Controls-Replacement guide to get to the ribbon cable.
check the actual switch if it look's corroded (white/greenish) or i any way damaged. those switches are simply thin metal plates, secured by a plastic strip/scotch tape..
if you find some corrosion (check the connector of the cable too) - clean it with isopropyl alcohol (>90%) - if the metal inside the switch is black, use a needle to "scratch" it carefully of the metal - don't bent the thin metal to much
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