There are a fair number of TV's on the market with ethernet ports, but which presently lack the firmware to allow them to be 'networked'
- indeed some
of them have firmware that doesn't even contain code for the RJ45 port, it's just a gimmick at present...
Equally it applies to certain tuner boxes, which have network sockets, but absolutely no functionality!
In any event, if your TV's ethernet port does work... it'd need to be connected to the router by network cable, and not plugged into your laptop's network port