The up to date software is probably the problem. Do this:
To downgrade, you'll need to download the previous software version here: ATV3 http://appldnld.apple.com/AppleTV/041-4361.20120605.grjot/AppleTV3,1_5.0.2_9B830 _Restore.ipsw
ATV2: http://appldnld.apple.com/AppleTV/041-4362.20120605.t8i4U/AppleTV2,1_5.0.2_9B830 _Restore.ipsw
Next, plug the Apple TV into your computer with a micro-usb cable (most phones today use these) and start up Itunes. It should detect the Apple TV in recovery.
After that, hold down Option on Apple or Alt on Windows and click Restore. This should open a window that allows you to select the software update you want to apply. Select the one you downloaded earlier.
It will then go through the restore process, which takes only a few minutes, and then you will be able to plug the Apple TV back in to your display and set it up again.
You will only have to do these steps once to recover the Apple TV, and it will give a message after it's done that it's ready to be set up again. After setup, make sure you don't update the software again.
I recently ran into a similar issue with a bunch of these things and after restoring them all to the previous software version they are working again.