Make sure that LW's being allowed thru the XP firewall. This link has some info.
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Update your Java & try this version. Use the JRE offline installer & remove your current Java version before you install this one.
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Next, delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
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This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.

Your modem doesn't have a firewall...do you have a router as well?

If none of that helps, follow foolofthehill's advice here for uninstalling LW & removing all traces of it.
http://www.gnutellaforums.com/283346-post2.html
Once you've done that, reinstall LW & make sure to use the offline installer. When you click to download LW & the download box pops up, cancel that. Now you'll see an option to download the offline installer
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