Do any of the other places that you use LW successfully have a Tiscali connection? Tiscali are a pain. Read the threads below for more info. Try connecting outside of peak hours.
Tiscali & Limewire
can't connect between 5pm-11pm
I have found a solution to getting Limewire to work with Tiscali

If Tiscali are causing the problem (some people just can't seem to connect & some eventually can), there might not be much you can do. One of those threads above tells you how to change ports...see if that works for you.

What version of Java are you using? Heaps of people have had trouble using LW with Java 1.6.0_01. Try this version instead. Use the JRE offlilne installer & remove your current Java version before you install this one
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

What's the model of your D-Link? It might have it's own internal firewall.