Make sure that LW's being allowed access through the Windows firewall.

Try the advice here: all of a sudden will not connect (a fix to try)
Start off by deleting LW's preferences folder & changing Java versions. Read the whole thread.

Things are a bit different for Vista when finding the preferences folder & other files/folders within Application Data. This thread should help with that: LimeWire Pref Folder in Vista
You'll know if you've deleted the preferences folder properly...when you start LW, you'll go through the setup wizard again & all the settings within LW's options will have changed.

If nothing there helps, try to find out the brand & model of your modem/router. If nothing's showing on top of the device, have a look underneath.