When your Limewire tries to connect are you getting any connection attempts ?
Press the connections tab:
Attachment 2904
If you don't see it then press View>Show/Hide>Connections
Attachment 2905
It should look like this:
Attachment 2903
Until:
Attachment 2906 Just kidding Limewire Basic will connect to 3 UltraPeers and Limewire Pro will connect to 5 (Unless running as an UltraPeer yourself.
If Limewire is totally blocked for some reason it will look like this:
Attachment 2902
Did this make any sense ??
Also like OAH said it could be your ISP blocking Limewire. And also it would help a great deal if you could tell a bit more about how you connect. Like what does your LAN card connect to and are you sharing your internet with anyone (eg. live in an apartment building)