1. Connection type?
2. Modem & router brand name & model numbers?
3. Where are you trying to connect from (home, school, work, etc.)?

Have you tried these suggested fixes: Fixes for Limewire

Many high speed modems have internal firewalls that not everybody is aware of. If we know your model then we can determine if this is any type of issue or not. Also whether you're going thru a network at work or school, etc.