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.
Customer surveys are for companies who didn't pay proper attention to begin with.