Find out whether you're using a software firewall (Win ME doesn't have one built in) If you are, you'll need to make sure it's configured to allow LW. If you're not using a software firewall, I'd recommend that you get one! There are some good, free ones around.
FREE Firewalls for Windows - Free Firewall Download
A Google search will bring up more results.

Try this version of Java. Use the JRE offline installer & reomve 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...well, who knows...can't find any info about that model It doesn't even show up on the Linksys site. I'm guessing it has a firewall. Have a look at the list of Linksys routers here, you might be able to find one with the same setup pages as yours. Or, check your manual to see if there's any info about port forwarding (to get rid of the firewall icon).
PortForward.com - Free Help Setting up Your Router or Firewall