Agree that anything bearing the name Symantec / Norton is worse than a waste of time. Uninstalling it through the programs menu on the control panel should kill it, otherwise there are freeware utilities (google) that go through the registry and remove stuff for you.
This particular problem, however, sounds very much like a problem with your Flash player (Youtube plays videos through it). You can download the latest version here:
Adobe - Install a different version of Adobe Flash Player
Also, not using Internet Explorer (Chrome or Firefox are vastly better) will also help.
