The LED light in front comes on, but no signal is coming out. I plug my Xbox and Blue Ray player into the same HDMI Cable and they both work fine. The Apple TV was working fine, then one day it came on but no video.
In that case, you may well probably be right and the Apple TV may well have failed. Personally, I would probably just purchase a new Apple TV, however have you enquired with Apple as to how much a repair might cost, or indeed have you obtained any other prices from any other third-party repairers.