Here are the two things I would do to debug this problem.
1.) Use the Tomcat Manager application to see if your application has been deployed.
http://localhost:8080/manager/html If you haven't already set up a manager username and password, you can do so by editing the tomcat/conf/tomcat-users.xml file.
2.) If it hasn't been deployed or if it has but still isn't showing your page, look at the Tomcat logs under tomcat/logs.
If there are a lot of log files in there or if the files are large; stop tomcat, delete all the logs, start tomcat, try hitting your page again, then check the logs if it doesn't work.
You should either see some deployment errors or some runtime errors.
I'm guessing, since you said that you've put a web.xml file under WEB-INF that there could be an xml syntax error in that file that has kept your application from being deployed correctly. The logs will point this out to you.