Streaming from PC to TV

Currently, I have a one port router in our living room right behind the TV, a Panasonic Viera with a mysterious unused ethernet port amongst others. The router's connected to the internet, and then an ethernet cable which is embedded in a wall running into our only computer in the next room. I'm running Windows 7, and I have a codec pack installed to play DVDs and other stuff.

I'd like to turn the PC into a mini media centre for the TV, but without moving it or building a dedicated one. I've heard about streaming media from a PC to a TV, but I don't entirely know how to go about this. I'd rather there are no other cables running between the rooms, and don't own a 360 or a PS3 (I don't really want to get one either). It would be even nicer if streaming HD content is possible. I'm willing to get a two or more port router.

I have a ~3.0GHz dual core AMD processor, 5GB RAM, and an NVidia 9400 GT 1GB graphics card.

My question is this: Can I do it, should I do it, and what is the cheapest way to do it?