FAIL - Deployed application at context path / but context failed to start

Context Path (or) Context Root must be unique for each application deployed on the server.

So you can't deploy two applications with same context root to the same server. It seems for both of your applications the context path is /.

Check server.xml to see what context path both of them have. If they are not unique, then change them to solve the problem.

But if you want the same context root for both applications, then you need to deploy them in two different servers.

For more information: Tomcat Context paths configuration

I may be a little late but would say that this could be because of the change in the factory name in Tomcat 8. So follow the below steps:

1) First, see if you are using Tomcat 8 or higher.

2) If yes, and tomcat is not able to deploy your application. Run the application in Debug mode and see stack trace in Tomcat window (at bottom. Not same as Tomcat.log). Scroll down the window and see if you can find an Exception like this:
Caused by: java.lang.NoClassDefFoundError: Could not initialize class org.apache.tomcat.dbcp.dbcp2.BasicDataSourceFactory

3) If you see something like above, Open your META-INF/context.xml and replace or add the factory attribute in the resource tag with: factory="org.apache.tomcat.dbcp.dbcp2.BasicDataSourceFactory"

4) Restart tomcat and redeploy.