Welcome to the Apple Community.
If your problem persists get yourself a micro USB cable (sold separately), you can restore your Apple TV from iTunes:
- Remove ALL cables from Apple TV. (if you don't you will not see Apple TV in the iTunes Source list)
- Connect the micro USB cable to the Apple TV and to your computer.
- Reconnect the power cable (only for Apple TV 3)
- Open iTunes.
- 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)
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- Check that you have correctly followed the instructions for your model of Apple TV.
- If not already, try using a powered USB port.
- Repeat the process but this time try connecting the cable while iTunes is closed.
- Repeat the process with another cable.
