Wow, really old stuff. And yes others have come across this same situation with the newer JBoss Tools and more recent versions of Eclipse.
First some background. When Eclipse starts the app server, it monitors the Server MBean to determine when the server has fully started. To do that, it needs access to the JNDI port and the JMX ports.
Eclipse can fail to recognize that the app server has started if:
a) You change the JNDI or JMX ports
b) You have the app server bind to an IP address other than localhost (or 0.0.0.0, which is the default in 4.0.5)
c) You secure the JMX invoker, in which case Eclipse does not have access rights to JMX
d) Your hosts file has an incorrect address for your system (if, for example, the DNS assigned a different address). One person actually had security set on the hosts file so that it was inaccessible.
Those are the possible issues that come to mind.
One thing to try is bring up the app server from the command line and then attempt to use the twiddle utility to access the Server MBean - if you you do that then Eclipse should be able to.
I might even try using JDK 5 instead of 6, especially since 4.0.5 is not qualified with JDK 6.