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.
Java EE 7 Workshops: Bootstrap, Effective, Architectures, June, 13th-15th, Munich's Airport
On demand workshops: Java EE 7 Bootstrap, Effective Java EE 7, Java EE 7 Testing and NEW: Java EE 7 Microservices are available for streaming