Turn off the Windows firewall & configure Norton to allow LW.
PortForward.com - Free Help Setting up Your Router or Firewall

What version of Java are you using? Try updating to the latest version here. Use the JRE ojffline installer & remove any other Java versions installed on your computer, before you install this one.
Java SE Downloads

Did the port test work?

In LW, go file > disconnect. Wait 10 minutes, then file > connect.

Are you using a modem/router? If you can find your device on the list here, try port forwarding.
PortForward.com - Free Help Setting up Your Router or Firewall
Don't forget to set up a static IP if that's part of the instructions. LW's listening port, port in the 'manual port forward' box & port forwarded within the modem/router should all be the same number.

Did you delete LW's preferences folder? You'll know if you deleted that folder properly - when you start LW, you'll go through the setup wizard again.

If it's still not working, try the fix here (replacing gnutella.net file).
all of a sudden will not connect (a fix to try)
Those instructions are for XP, but you'll need to open LW's preferences folder called LimeWire...the same one that you deleted earlier. Then remove & replace the gnutella.net file there.