I resolved the issue.
When I created the Server, the default value of the Server Name field is "JBoss EAP 4.3 Runtime: jms1 Server". I get a NoClassDefFoundError: org/jboss/Main when I try to start the server.
I deleted the Server. Then I created a new Server with the Name, "jms1". Now when I start the server I get a different error, "org.jgroups.ChannelException
: failed to start protocol stack, Caused by: java.lang.Exception: exception caused by UDP.start(), Caused by: java.lang.Exception: problem creating sockets (bind_addr=localhost/127.0.0.1, mcast_addr=230.1.2.7:45577), Caused by: java.net.SocketException: An operation was attempted on something that is not a socket".
I get this same error several times in the Eclipse Console.
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After appending the string " -Djava.net.preferIPv4Stack=true" to the VM Arguments textarea of the Launch Configuration for my "jms1" server it starts up with no errors and Eclipse detects that the JBoss server is running!