First see: Operating Chat through a Firewall, and Error message "cannot connect to chat server".
Assuming all the above have been addressed, and you succesfully have other users chatting with the JAVA client, then the problem is still one of users' firewalls AND/OR proxy servers.
Many ISPs run caching proxy servers on their networks in order to improve the apparent performance of their system. The problem with this is that it does not permit the two way communication required by the JAVA applet. One possible way around this is to set up your chat to use a port other than 80, but then of course you might shut out users whose firewalls will not permit connections other than port 80.
The next possible block is the user's firewall. Even if port 80 is opened for traffic, many firewalls are configured to not permit non-HTTP traffic over it (IOW...the two way communication the JAVA applet requires).
In both of these cases, if the proxy cannot be bypassed, turned off or otherwise tuned to permit two way communication, or the firewall cannot be changed to permit non-HTTP traffic over port 80, then the user(s) in question will have to use the HTML chat option as a fallback. It is for just such situations that the HTML chat option exists. You will need to turn this option on in your Chat Services Control Panel, and then the user(s) will need to pick HTML Chat in their personal Preferences.
Note: HTML chat and "moderated" or "hosted" chat events (where you have audience, backstage and stage rooms) are not compatible. For this JAVA is the only possible option.