can't turn on apple tv without unplugging power cord and then plugging it in again.
How can I turn on my Apple TV?
Only thing that works is to unplug power and then plug it back in.
Apple TV (3rd generation), iOS 6.1.1
This is likely to be the result of a bad HDMI or network connection, are you able to test the device in another location to try to narrow down the possible problems.