You've already tried the 'unpaid remote' sequence which can help if AppleTV for some reason thinks another remote is controlling it, but it seems it wasn't that.
I think you'd be best restoring it using a USB to microUSB cable connected to a computer running iTunes, see:
Apple TV (2nd and 3rd generation): Restoring your Apple TV
If that doesn't work/help, and it's under warranty get Apple or store you bought from to replace it.