Are you sure that you used 4.12.10 last weekend? AFAIK it hasn't been released for that long. Maybe it was 4.12.6??

Don't run without a firewall. Make sure that the XP firewall is off & just configure McAfee to allow LW...double check all of your settings.
How did you have your LW set up before for your router...UPnP enabled, port forwarded or neither (I know this doesn't mean much if you can't even open LW but the info might help someone to sort your problem). Also try & find out the brand & model of your router.

Just try updating your Java (btw going to add/remove programs & finding Java on the list should tell you what version you have). Use the JRE offline installer & remove your old Java version before you install the new one. See point 1 below
Fixes for LimeWire

4.12.10 seems to set all options back to default on install so I really am not sure if it's any use deleting the preferences folder. Maybe someone else could tell you if that would help or not

Edit - you could also try the Java 1.6 JRE & see if that makes any difference.
http://java.sun.com/javase/downloads/index.jsp
I think you'll have to make sure there are no other Java versions on your computer for this one to work.