In JEE 5 servers like JBoss and Glassfish, the jsf-impl classes are provided by the server. However, with Tomcat, you have to include a jsf-impl.jar in your WAR. In Tomcat 5.5, I think you may also need an el-impl jar (Tomcat 6 provides one, but not Tomcat 5.5).
You can use any JSF standard core implementation to provide the jsf-impl jar. I've used both the Run RI and Apache MyFaces. Either one works well.
An IDE is no substitute for an Intelligent Developer.