Finally decided to join the streaming world with my 2009 Sony. Acess to all sites (Neflix, Amazon, Hulu) failed. Broweser access failed with Opera error 70. I was using hardwired ethernet connection. The network diagnostics showed I'd received an IP address and other DHCP info from my router, and logging into my router verified the connection to the TV. Both errors seem to indicate that the physical and logical network connections are fine but that a secure (SSL) connection was failing.
The TV had automatic software updates enabled. When I tried a manual update it failed connecting to sony.com. I noticed that my TV was running a software version starting with PKG3, Sony's support site showed the current version started with PKG4. Notes for the PKG4 release stated it changed the SSL3.0 (secure socket layer) software. I ended up following the USB update instructions found here - https://www.sony.com/electronics/support/lcd-tvs-legacy-lcd-tv/kdl-55ex720/downloads/W0010145. This meant downloading the update to my PC, transferring them to a thumb drive and sticking it in the USB1 port (USB2 port didn't work) in the TV and waitching it update (took 5 minutes). This resolved the problem.