Who is your ISP by the way? Could you try to download a magnet link as an experiment to see how fast you get:
http://www.magnetmix.com/video.shtml
Tell us what happens in regards to speed, connection, etc.
For downlding music, see the tips here
How to find music
Edit: oops sorry I forgot you can't connect. Try deleting your LW Preferences folder whilst LW is
closed; instructions here:
Point #2 & 3 in Fixes for Limewire (sample image included at bottom of page.) Then next time you open LW you'll be requested to set up all options again. So make a note of them before deleting your LW prefs folder. You'll also need to reset your connection options such as
Manual port forward instructions & sample image. But use the port you port forwarded with.
BTW sometimes it's better to set LW to open without connecting, then manually connect after 5-10 mins by choosing Connect under File menu. To do this if you want to try, the option is Tools>Options>Connections & choose not to connect on start up.