We also have a computer underneath the TV, about ten to fifteen meters away to the back of the house. At first, I had created a cable and looped that through the plinth to where the computer is, but either that cable is of low quality or my plug crimping skills are insufficient, because we've only had really slow connectivity there. Then I plugged in a wireless card and relied on the wifi, but that had spotty reception at best -- not ideal when you're watching streaming video or playing a game online. Then I bought two of those homeplug adapters. That worked, and we had good throughput, but with high throughputs the adapters crashed and needed to be taken out of the socket for a reset. Workable, but certainly not ideal.
So I bought a 20m cat6 ethernet cable, and simply ran a cable through the house. I bought a cable with a brown sleeve, to color-coordinate it with the plinth. It was a bit of a hassle to run the cable behind the bookcases and all, but with the two of us working together we had it done within an hour. I didn't want to run the cable through the plinth, because we have foil pinths that you attach to a slat nailed to the wall with tiny nails. I suspect the first cable fiasco was due to a nail going through the cable, and I didn't want to run that risk again.
So we went for a bit of a ghetto solution: hot glue. A big dab of hot glue on top of the foil plinth and simply press the cable in there when it cools a bit. And since it runs behind bookcases and other things for most of the way anyway, that's just the right solution. And who knows, if we want something else further down the line, it's easy to dissassemble too.