If your getting search results you have to be connected. Did you do this, In limewire go to Tools>Options>Searching>Basic> then tick the "Show License Warning" box, then click apply.
The next time you go to download something the "License Warning" box should pop-up. tick "Always use this Answer" then click "yes". You should be able to start downloading.
If none of that works you may have to port forward your router.
http://portforward.com/routers.htm Follow the instructions. It's very important to set up a static ip first.