I bought a Chromecast yesterday, and I have no evidence that it does anything on my TV. I plugged it into the HDMI socket of my 2005 vintage TV - a socket which works, because I can show my computer desktop on the TV, through an HDMI cable and adapter. The TV doesn't recognize the Chromecast, although I have the TV set to digital in. The Chromecast works on someone else's TV. I don't watch TV, and just have this old TV kicking around, so I'm thinking that Chromecast just isn't for me.
I've checked the router settings, I've tried Chromecast with the included extension lead, I've tried it while I have been pushing it into the TV, in case there was a lose connection. There is only one HDMI socket, by the way.