Q: Apple TV light flashing rapidly and won't work

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If your problem persists get yourself a micro USB cable (sold separately), you can restore your Apple TV from iTunes:

1. Remove ALL cables from Apple TV. (if you don't you will not see Apple TV in the iTunes Source List
2. Connect the micro USB cable to the Apple TV and to your computer.
3. Reconnect the power cable (only for Apple TV 3)
4. Open iTunes.
5. Select your Apple TV in the Devices list, and then click Restore.

(You may already have a micro USB cable if you have a camera or other digital device)

If you see the "Connect to iTunes" screen on your Apple TV - Apple Support

As an addition to Winston Churchill's answer, here's the official Apple manual for that action with a picture of a micro-USB cable.