Try changing your Java version. Remove your current Java & then reinstall, use the JRE offline installer.
Java SE Downloads - Previous Release - JDK 5

After that, delete LW's preferences folder when LW's properly closed. See point 3 below (also point 2 if you've used much older versions of LW in the past).
Fixes for LimeWire

Your router has a firewall. If the router supports UPnP, enable it & choose the UPnP option within LW's tools > options > advanced > firewall config. If that doesn't help then you could try port forwarding. Here are the instructions for your router.
Port Forwarding for the Dlink DSL-G624M

Don't forget the step of setting up a static IP, else port forwarding won't work LW's listening port, port in the 'manual port forward' box & port forwarded within a router all have to be the same number