If you are receiving a "404" error, Tomcat has most certainly started. You just don't have a proper webapp deployed.
Actually, let me qualify that. The Tomcat "404" page is sort of a bluish-green header and says "Tomcat" in the page text. If some other web server (such as Apache httpd) had grabbed Tomcat's HTTP port, that server's 404 page wouldn't say "Tomcat" on it.
An IDE is no substitute for an Intelligent Developer.