Hello!
First make sure that you are actually connected to the Internet!
Do you have a FireWall at your home or included with your internet service provided trough your ISP?
If it turns out that you are connected trough a FireWall then open the ports 6346,6347 and 6348 for out and incoming traffic for LimeWire and Gnutella.
Have You updated your Java Runtime Environment?
If you have not then you should go to Apple's website and update MRJ to the latest version which is 2.2.5
http://www.apple.com
And if all this fails then try to download and install a new copy of LimeWire 2.4.4 which is the latest version.
If it still wont function then it is possible that your ISP are blocking Port 6346 at their servers so that you cannot use Gnutella.But hopefully this is not the case.