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.
NEW workshop: Building HTML 5 Applications Without Frameworks, Full week in December 2016: from Java EE 7 Bootstrap, Effective, Architectures over Testing to Microservices
On demand workshops: Java EE 7: Bootstrap, Effective, Testing and Microservices available for streaming.