Make sure your Windows firewall's configured properly.
Firewall setup

Do you have your own router or modem? Or do you just connect from the computer straight into the wall? If you've got your own router/modem, have a look for model numbers (look underneath as well).

Has LW stopped connecting since you updated Java? Or has it worked properly with Java 1.6.0_01 before? Try this version of Java. Use the JRE offline installer & remove your current Java version before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.