How to start Neo4j on Azure
The problem has been solved with help from Neo4j support. Hopefully they will fix the bug so you will not face this issue. For some reason one line was not in the template used to install the Neo4j VM.
The problem was there was not a listener for all the Neo4j ports in the neo4j.conf file. Make sure they are there for all three ports (7473, 7474 and 7687). The format is:
dbms.connector.bolt.listen_address=0.0.0.0:7687

You might also need a default listener:
dbms.default_listen_address=0.0.0.0

Other insights learned in debugging this:

When you restart the VM, it may take several minutes for the Neo4j
Browser and python code capabilities to recycle and come up.
In Putty, the command &quot;neo4j status&quot; will return &quot;neo4j is not running&quot;
even when it is.