It's frustrating when you pay for something which doesn't work as you'd hoped but...you could've got the basic version & not paid a cent

Have you configured your firewall to allow LW access?
http://www.limewire.com/english/content/firewalls.shtml

It's important to find out your modem/router info as this is often the cause of connection probs. Your modem is the thing that plugs into your comp & lets you connect to the net. Have a good look around at all your hardware.