It sounds like Verizon is the culprit here, if limewire works on your laptop at work, it's not a fault with that....It maybe your port forwarding set up, but I doubt it...
The give away is Do this simple test for us. Using your browser go here:
http://www3.limewire.com:6346/ The page should say 'Your test worked!'. What happens when you go there?
Page not found / Cannot display page. Normally when you see that it means that your ISP is shaping your connection to p2p sites....
These are your step by step instructions for port forwarding your Netgear router....See how you go with them....
Port Forwarding for the Netgear WGR614v6