If the port 6346 test isn't working then something is blocking LW's default port. Usually it's an ISP but I can't find anything to actually say that Verizon's blocking p2p. Maybe you should call them & find out why port 6346 is blocked!

You could try changing to a higher port, try one in the range of 49152 - 65535. If you change ports, you'll also have to change the ports allowed within your firewall & any ports forwarded through your router... were you port forwarding when LW used to work? Your modem does have an internal firewall so you'd probably need to port forward. There's info here if you need it:
http://www.portforward.com/english/r...l6100index.htm