Q: Will air share work on a wired home network?

I have a iMac and an AppleTV hooked to a flat screen TV in my office. They are wired, not wireless. They are connected to my fiber optic modem/router which is in an adjacent building (my home). In that building's living room I have another Apple TV and flat screen tv. They are also wired  to the same fiber optic device. Both of my Apple TV's are the 2nd gen versions running the latest updates. This is my problem. The ATV in the office works perfectly. The ATV in the living room cannot see my "home sharing" network. It sees everything else but always gives me a message that I need to turn on "home sharing", It is turned on, and iTunes is running on my desk top iMac in my office. I cannot determine how to get it to work. I have switched the ATV devices and whichever one I install in the living room, it will not see home sharing. So I don't think the ATV's are at fault. I believe the wiring is good because it sees movies that I can rent, tv shows, you tube and so on. The network connection checks out good when tested on it. I've tried it both wired and wireless and it still won't see the home sharing feature. When I first set up this system it did work perfectly and I've not added or removed any devices, but it stopped seeing the home share. Everything has been reset over and over and all my username and password info is correct. I have noticed that the only devices that appear in the lower left corner of iTunes is 'Computer" and "living room TV". The ATV in the same room doesn't show as a choice even though it works perfectly.

The other problem which may be related is that on my iPad 1st gen device I can no longer see the air play icon. I've reset and it does not appear. I feel that I've inadvertantly changed a setting somewhere that has now stopped these two devices from working correctly. If anyone can suggest anything that I have'nt already tried I would be most appreciative. I don't know if the air play feature will work with a wired network?