Make sure that the Live OneCare firewall is configured to allow LW.
Windows Live Help

If you're using McAfee VirusScan Plus, there's a firewall included, so in that case you'd have to choose between the Windows & McAfee firewalls...disable one & configure the other to allow LW.

Some people have had connection problems with the latest Java updates...try this version instead. Download the JRE offline installer & remove any other Java versions before installing this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

There's a firewall in your router. Try port forwarding, the instructions are here.
Port Forwarding for the Linksys BEFSR41
You'll need to set up a static IP first, there's a link within those instructions. LW's listening port, port in the 'manual port forward' box & port forwarded within the router should all be the same number.