You could run a cable from the PC to the TV, but it is not very practical is it?
First you will have a big long cable running through the house.
Secondly you could only control the iPlayer while sitting in front of the PC, so you would have to keep running back and forth between PC and TV.
So I would suggest:
1) Assuming you already have broadband, and if you have not got one already, get a ROUTER.
You may already have a router without even knowing it. It is what you plug the cable in from your PC to get broadband.
It MAY just be a modem, but you need a router. And most modern routers have wi fi built in.
2) Once you have a router get a laptop. You can get any cheap laptop that is wi fi enabled (even second hand).
You can then sit on your comfy sofa with the laptop on your lap, controlling the iPlayer, and watching the image on the TV.