I want to connect my home computer to my work computer. I want to be able to play some YouTube videos and be able to hear that sound on my work computer. To connect, I want to use TeamViewer. I do not want to use the microphone on home PC.
You can't use TeamViewer because it doesn't transfer audio, as well as the refresh rate is terrible. Splashtop Remote (http://www.splashtop.com/) remote however is cheap, and gives you both sound and good quality video, and there are trial versions available to see how it works out for you.
Alternatively, since you obviously just want to bypass your workplace web filter, look into online proxies such as http://hidemyass.com