I'm finding Limewire 4.14 to be dragging the life out of my computer as well, I'm having difficulties loading pages...
But onto your connection problem...It could be a Java issue try uninstalling all versions of 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
Have a look at these tips as well...
Frequently Asked Questions - LimeWire
You could also try this...
Go to your connections Tab in limewire, if it's not showing up go to Veiw > Show/Hide and make sure the connection tab has a tick next to it...
Then click on the Hosts and remove them and let Limewire search for some more...