This has worked for a few Vista users: Uninstall LW (start > all programs > LW > uninstall) & ZA. Now reinstall LW first. Finally, reinstall ZA. Installing LW before ZA seems to be the trick
Double check that the Windows firewall's off.

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

If you still can't connect, delete LW's preferences folder when LW's properly closed. You'll need to show hidden files & folders to be able to find the preferences folder. There are instructions here.
LimeWire Pref Folder in Vista
You'll know if you deleted that folder properly - when you start LW, you'll go through the setup wizard again.

Try port forwarding for your router, the instructions are here.
Port Forwarding for the Belkin F5D7230-4
Don't miss the step of setting up a static IP address. LW's listening port, port in the 'manual port forward' box & port forwarded within the router setup should all be the same number

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.