You really need to include more details about your system.
If not then every answer will be a shot in the dark.

Only you know how you are connected to the internet ? We are not psychic here on the forum and therefore can't tell you what kind of modem/router you have

1. What's your connection like - do you have any green bars at all?
Is there a brick wall in front of world ?

2. Do this test & see if it works. What does it say ?
http://www3.limewire.com:6346

3. What are your details

OS ? (Win XP, Mac OSX etc.)
How much free harddiskspace ?
How much RAM ?
LW & Java version ? (In Limewire press Help>about LW & you'll see)
What Firewall you're using ?
Modem/router brand & model ?
ISP (Internet Service Provider) ?
Connection type ? (modem, DSL etc) + Speed Up/Down if you know
Where you connect from (home, school etc)
Are you sharing a connection with other computers
Has Limewire ever worked for you ? If so how long have you been using it ?

Have you tried using any other P2P apps & if so, do you have the same problems ?

Also include any attempts to fix this. It helps people rule things out