The 360 was on during the power outage.
Hello LAPIII. I'm sorry that your 360 won't turn on. That would frustrate me, too. Here are the troubleshooting steps you need to perform on the power supply. It may be that the power supply is dead and you'll need to order a new one. A link on how to order a new one is also on the same page: support.xbox.com/.../check-power-supply. Good luck and hopefully it's the power supply and not the console.
something else worth trying is removing all the cables from the console, press the power button on the console several times, reconnect the cables and try it again.