I tried following the instructions that Birdy gave, but that did not work either. All firewalls have been turned off or LW has been allowed. Any other suggestions? The only thing that I have not done has been to uninstall/re-install LW.

When you deleted the preferences folder, did all of your settings within LW's options change? The first time that you started LW after deleting the prefs, did you have to choose a location for saving downloads?

Try uninstalling LW (start > all programs > limewire > use the uninstall option) then use your comuter's search to look for all files & folders with limewire in the name & delete what you find.
If you've changed your location for saving, make sure that you're not saving downloads to somewhere within LW's files or you'll lose your downloads when you uninstall LW! Also, if your downloads folder has limewire in the name, don't delete that one after a search!!

Once LW's all gone, reinstall & make sure to use the offline installer. When you click to download LW, cancel the dialog box which pops up...now use the option to download the offline installer. Once LW's installed, restart your computer. Then start LW & see how it goes.