Can you give us a total desciption of your set up:
1. OS version,
2. What firewalls you have,
3. ram, 4. HDD space available,
5. Connection type,
6. Modem & router brand name & model numbers,
7. Where are you trying to connect from (home, school, work, etc.)?
These details are vital if you want us to find out what your connection problem is.

Some things to do:
Get the most recent Java: Java 1.5 (take the JRE)

Do this simple test by going here: http://www3.limewire.com:6346/ It should say 'Test Page was a Success'. What happened when you went there. It tells us whether the port LW uses is totally blocked for you.