You can't get a virus just by opening a web-page unless you're using a very old version of IE, or have disabled all the security options in IE.
What is more likely is that youtube had nothing to do with it. You already had the virus and AVG happened to come across it at the time you were watching the video. When AVG tried to remove it, it triggered the virus.
In fact, the virus had probably got itself into the boot-up sequence already, pretending to be a core component of windows. When AVG removed it, it removed part of the boot-up sequence, and so now you can't boot up
[b]
