As far as I know, Avast! doesn't include a firewall...even in the paid versions If you have the free version, there's no firewall. If you have a paid version, just double check to see whether there's a firewall. If there is, make sure that it's configured to allow LW. If there's not, make sure that the XP firewall's configured to allow LW.
User Cant Connect - LimeWire

Pipex are known for traffic shaping. Not so sure about port blocking but it's possible. Within LW go tools > options > advanced > firewall config. Change LW's listening port to 64049 (or ports in the range of 49152 - 65535) > Apply > ok.
Have you tried connecting outside of peak hours? Give that a try.
Pipex have a FUP during peak hours.
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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

If that doesn't help, 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.

Your router might have it's own firewall & so you could try port forwarding. Have a look at the Zoom models in this router index. Find your model & then choose LW from the list of programs...you'll then get instructions for port forwarding.
PortForward.com - Free Help Setting up Your Router or Firewall
LW's listening port, port in the 'manual port forward' box & port forwarded within the router all have to be the same number