Ok a couple of things to try...Do one at a time..
Try deleting your preference folder...
Fixes for Limewire when LW isn't operating as it should
Try uninstalling your Java from the add/remove programs and then re-install the JRE 5.11 offline version....
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11
If those fixes fail could you tell me the model numbers for your modem and router, you will find the info underneath them...