My 32EX600 Sony Bravia TV is Ethernet connected to my Mac Mini, which is part of my Airport network, together with another Mac, an Airport Extreme Base Station and an ADSL modem/router. Moreover, the Mac Mini is connected to the TV by HDMI.
Whatever I tried in the TV’s Wired Network Set-up (Auto, or Manual with manual IP, Subnet Mask, Default Gateway and DNS IPs), I couldn’t get it right. Cable Connection and Local Access were mostly OK, Internet Access always Failed.
The solution lies in the Sharing panel of the System Preferences of the Mac Mini. In the Internet Sharing item of that panel, you should choose to “share your internet connection from WiFi to computers (the TV in this case) using Ethernet“, and NOT (as I had chosen before and seemed so obvious) “share your internet connection from Airport to computers using Ethernet“. After that change, the Bravia Network Set-up, using the Wired and Auto options, flawlessly connected to the internet. No expensive (Sony) WiFi USB dongle needed.