Some people have had trouble connecting with Verizon recently. If it's an ISP issue there's really not a lot that we can do. Since you're having trouble with other p2p apps, it's possible that the problem's with Verizon & not LW

Things to try:

Change ports. In LW tools > options > advanced > firewall config. Change LW's listening port to 64049, or something in the range of 49152 - 65535. Apply > ok.

Download the 4.13.2 Beta version of LW & see if that connects.

Your router has a firewall. Try port forwarding. Here are the instructions for your router.
http://www.portforward.com/english/r...4/Limewire.htm

Don't forget the step of setting up a static IP. The port forwarded through the router, LW's listening port, port within the 'manual port forward' box must all be the same number.