Two days at trying to get Limewire to connect, and tried every variation of Port forwarding, router set up, firewall on and off, Trashing prefs. reinstalling Limewire, Trashing prefs again.
I read and re-read the postings relating to connection woes. Blamed ISP, Router, Limewire, Dog. Coffee ran out. couldn't tie the knot in the noose--Get the picture?

Limewire opened but got to the first bar in the connection display, and then the dreaded"You may not be connected to the Internet, or you have a firewall blocking ............." message. every time

Mac OSX Tiger 10.4.3 with Firewall enabled +Passive FTP mode in Network prefs

Checklist:
1. Test worked
2.1GHz power PC 768 MB RAM
3. About 40 GB
4.ADSL sub broadband =512KBps upstream 212 downstream (Sorta)
5.Netgear DG834G wireless/ethernet router WITH FIREWALL as well
Ports congured in router for Limewire : Outgoing. ANY. Incoming 7856 (See edit below)
6.Home LAN -
7.Limewire version 4.9.37 Java 1.4.2_09 downloaded yesterday with most recent Java (1.3.1 and 1.4.2 release2+J2SE 5.0 release 3)updated through Software Update
8. Pipex - low end broadband due to line provider only giving 512KBps
9. 4 Macs and no other p2pp progs other than Limewire on 1 Mac
10. used Limewire some time ago but have upgraded the OS several times since.
Yes. I am an experienced Mac user. Human as well.

MY SOLUTION:
Quit Limewire.
Trash Prefs: User name>library>preferences>Limewire (A folder) Ditched the folder
Note: Previously, the Limewire prefs (I thought) were a single .plst file. I might have missed the real one, or I had some left over from a previous Gnutella/Limewire, but dont think so.
Restart in Safe Boot mode (Hold down the shift key after hearing the gong)
While in Safe boot, Repaired Permissions- which were ok anyway.
I could NOT resist starting Limewire (Still in Safe Boot)It went through the language thing and download folder location stuff, which was the first time I've seen that this time. (Yeah--Preferences)

B..... me--- It worked

Quit Limewire, and restarted in Normal boot.
Fired Limewire up again..........It still works, and is downloading at 20 KB/s from 1 host

Conclusion: The initial connection problems were not resolved by messing with firewalls, other than configuring the router to allow outgoing and incoming Limewire traffic.

edit..UPnP in Limewire prefs is activated, which suggests that my attempts to configure the router, are wasted. Will retest

Having 2 firewalls doesn't interfere with the connection, as long as PASV FTP mode is selected in the Apple Network Prefs
The Firewall icon on the Limewire window still shows, even when it's connected through the wall
Ensure any Network filter, such as LittleSnitch allows Limewire Traffic obviously. (And there are loads of connections that it wants to make)

IMHO My problems were caused by the LW preference folder. Logically,nothing else helped.

Thanks due for all who have made suggestions. Sdaswani, I didn't run the .jar, just trashed the prefs folder

Cyclic