What firewalls do you have? What's the make and model of your router?
See whether changing ports helps. In LW tools > options > advanced > firewall config. Change LW's listening port to 64049 (or something in the range of 49152 - 65535) > apply > ok.
Try the fixes listed here:
Fixes for Limewire when LW isn't operating as it should!
See this thread for more tips:
http://www.gnutellaforums.com/connec...ere-first.html