So you've got an old TV or computer monitor with a VGA or DVI socket and it's looking pretty outdated because all the latest devices are HDMI only - including the cheap but amazingly great value Google Chromecast.
Well all is not lost! You can get a DVI-to-HDMI or a VGA-to-HDMI adapter and connect your TV or monitor to the adapter and then plug the Chromecast to the adapter. The adapter comes with audio sockets to take the HDMI audio and play it through the TV speakers. Really simple to put together and no software to set up.
VGA-to-HDMI Converter : $30 (or less on Amazon)
I have this setup on an old TV that was sitting in the garage. The picture quality is exceptional.