I slowed down and did some thinking and more reading.

The whole problem was that I had multiple entries for Java in the Control Panel, and the gnutella.net file downloaded with the application install is incorrect. The multiple entries for Java was because I "trusted" Sun's install process to do what it said it was doing and uninstall the earlier version.

Here's what I did, and now LW works properly:

1) I closed LimeWire, plus selected Exit from the LW icon in the system tray.
2) I uninstalled LW (Start/All Programs/LimeWire/Uninstall)
3) Opened the Control Panel and clicked Add or Remove Programs.
4) I had 4 entries for Java 6: Java 6, Java 6 SDK Update 1, Java 6 Update 2, and Java 6 Runtime Update 3.
5) I removed them all. (ignore the J2SE entries, they are for your IE browser)
6) I then installed the off-line version of Java 6. Now I only have Java (TM) 6 Update 3.
7) I then re-installed LW and started it.
8) I closed LimeWire, plus selected Exit from the LW icon in the system tray.
9) I copied the new gnutella.net file I had downloaded earlier into the LimeWire folder under the Application Data folder under my username. (the one that was already there was only 1kb in size, the new one is 21kb)
10) I started LW
11) After a few minutes, I now have a *Turbo-Charged Connection*