OK, here is my guess, based on the info you provided. You already proved your trbl is not w/you he gnutella network, as your desktop seems to run fine.

The firewall message you see is probably your modem/router firewall. It is a hardware firewall, much stronger than software firewalls. Sometimes these two firewalls can be a real pain in the a++s. Each brand of modem/routers configure things different, and a real good source of help can be found at portforwarding.com. Also verify network settings on laptop. Make sure you disable any traffic shaping services (ie, QoS)

Your java version could be a culprit, too. (not sure). I think your java version should be closer to the present version, at least 6.0 or newer. Maybe there is a way to use a separate java version for limewire, and the older one for your office.

You may want to post a HiJackThis log up here. This could help other forum members analyze your problem. Info on HiJackThis is posted all over the forum, just run a search for it.

Hope this gets u started