Can't access iTunes Library via my DHCP

Why can't I access my iTunes Library via my DHCP connection? It seemed to work sporadically at first, but now my library is consistently inaccessible with the following message: "Could not connect to 'NAME' Library. Make sure the computer is on the same network as the Appe TV, the iTunes version is up to date, and iTunes is running."

I've tried reconfiguring the network with the Automatic option, and then restarting everything. No dice. My wireless modem works, but it's too slow & keeps dropping the connection so is pretty annoying to use. It's why I got the Ethernet connection for Apply TV. It seems like it's something to do with my Ethernet connection specifically, but I can't figure out what. And no the firewall on my Mac has been turned off, I'm on the latest software etc., and my Internet service provider says it's nothing to do with them.

Has anyone been able to successfully navigate this problem?