I'd ask Apple Tech support what they meant by that request; the command(s) or sequence they expected you to follow. I wouldn't expect to hear that suggestion (nor do I know off-hand of an easy way to do that), unless there's something else going on here that hasn't been posted here. (There's a bunch of similarly-named giblets here, too, and Lion Server is somewhat worse in that regard. There's the server admin tool, server monitor tool, and the server admin daemon, and some other pieces.)
Do try connecting via Server Monitor and the LOM and rebooting the box. The server reboot probably won't resolve this condition though, as you've probably already tried that directly, or you've tried rebooting the server from some other mechanism or path.
More interestingly, try launching Terminal.app on the server (or ssh into the box, if that's available) and issue the following command:
sudo changeip -checkhostname
See if that tool reports success and no DNS changes required, or if it reports DNS errors with DNS changes being required. DNS errors are a common trigger for beach-balls within the server tools.
Also (at least for now) ensure that you have only one of the two network connections connected and active, or (if you have both going) that you have IP subnet routing set up and the connections are in different subnets. Network errors and routing errors can cause beach-balls, too.
Also take a look at the Console.app tool and the logs, or under /var/log, and see if there are any interesting errors. This to see if there are diagnostics related to the connectivity errors.