Thanks to other people who have mentioned that they are having the same problem. I noticed that I made a newbie mistake and didn't include my system information, so here is as much as I know:

Windows XP Home editon, McAfee Firewall, 768K RAM, 16.7GB available hard disk space, DSL Cable connection, Motorolla Surfboard cable modem SB4101, connecting from home, Limewire version 4.18.3, Java Standard Editon 6 (1.6.0_02), Comcast (provider), my test worked, no sharing, been using LW for a few years without this problem, no brick wall, Living in USA

I hope this information will help someone to offer us some suggestions. Thanks.