The Bug Report test would also be handy for both computers.

For Zone Alarm (& XP firewall) configuration to allow LW full access see: http://www.limewire.com/english/content/firewalls.shtml

By the way the red in your DC search results shows that you are firewalled at home by the looks of things. But then you might be firewalled at work. If you are firewalled your ip address will not show on LW when you select the direct connect search type.

See: How to Direct Connect, Browse & Chat