Welcome to the JavaRanch, Sean!
Actually, neither the StackOverflow question nor the one you posted here provides an extremely critical datum: what URL you were getting the "404" on.
When you deploy an app in
Tomcat using a context file in TOMCAT_HOME/conf/Catalina/localhost, the webapp context name you must use in the URL is the name of the
Context file and
not the context name
in the context file. This is very annoying to me, but that's how it works.
If you configure using a META-INF/context.xml in the WAR itself, the context name is going to be taken from the name of the WAR (I think. I'd have to RTFM). I don't recommend adding this item to an already-deployed WAR, though. Add it to the WAR build process.
Note that the conf/Catalina/localhost context will override any context definition done in the WAR itself.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.