My 2nd Gen Apple TV that I bought a couple years ago is not responding at all. Connecting it to every TV in my house does nothing. No picture, no audio.
Like the iPod nano, you can effectively "reboot" the apple tv by holding the down arrow and menu button on the remote. With the apple tv on (and unresponsive), reboot it as described above but be sure to keep the buttons pressed until the apple tv screen goes blank.
Of course, there is always a chance the batteries in your remote need to be replaced or the remote itself is broke.
If none of the above work then it is what is commonly referred to as "kaput".
Good luck.