Sometimes (often :-)) it is hard to say whether just the application or the whole application server is not working. Also debugging JNDI configuration may be challenging.
ping is a simplistic 5kb WAR which exposes JNDI, system properties and "echo" service through REST APIs.
Download the WAR. Source code is available at github: https://github.com/AdamBien/ping/
See you at Java EE Workshops at MUC Airport, particularly at: Effective Java EE 7!