That command won't show if it's listening on port 7071, try
Code:
netstat -an | grep LISTEN
instead. What does a zmcontrol status show?
[/EDIT] What was the result of your test with turning the firewall off? When you say 'it's not working' what exactly happens when you go to the admin ui? Can you telnet to port 7071? Are you doing these tests on the ZImbra server itself?