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The power outage may have also damaged your network card, assuming by your post that the system is cabled and not wireless.
Try another cable as Pete suggests.
Also check Device manager to make sure that the network card is enabled.
If running XP its start - control panel - system - hardware tab - device manager button
If everythign appears ok there and another cable does not work you may have to replace your network card as it may have taken a power hit. Its a cheap item. About 15 bucks at the most.