I've tried all the ports you suggested until the dialog box pops up stating that a firewall is probably blocking Limewire access to the internet.

I tried the test page as well, and none of the ports work while the same port was running in LW. Here is the detail log for port 1203:

Data dump: v1.7,to=5,ipf=no,ip=128.205.162.130,proxy=,port=12 03,lang=en,el=0,php=4.3.11

Start connection test for TCP...
Get socket.
Attempt to connect to 128.205.162.130 on port 1203.
socket_connect() failed, error 115: Operation now in progress.
(Ignore the previous error reason, it's a timeout instead.)
Close socket.
Done, return code: 'TIMEOUT'.

Start connection test for UDP...
Get socket.
Attempt to bind to 0.0.0.0 on any port.
Send /JCT: 3x12 bytes: GND\002sq\001\001\020JCT
Read response:
No proper answer received.
Close socket.
Done, return code: 'NOTHING'.

I just tried K-Lite v2.7, and it connects and works.
Any other suggestions?