Hi Jane,
Thank you for your assistance thus far and for not giving up on me! 
I ran the following test to verify that the cisco is actually sending out syslog messages.
I downloaded Tftpd32, it has a very simple built in syslog server that you can use. I installed it, ran wireshark and changed the cisco syslog destination from the zenoss server to my laptop interface IP.
I immedietly received syslog messages from the cisco and wireshark confirmed syslog messages sent from the cisco to my laptop!
I logged back into the cisco and changed it back to the zenoss ip address.
Neither Zenoss or wireshark picks up anything...
My laptop also connects to the same switch as the zenoss server with no firewall enabled.
This just keeps getting weirder and weirder... 
Any more tests to run?
I did what you reccommended and got this:
[root@localhost log]# ls -l origsyslog.log
-rw-r--r-- 1 zenoss zenoss 0 Apr 15 18:00 origsyslog.log
(Not looking good)
And so summerise:
[root@localhost log]# lsof -i -P | grep 514
python 14524 zenoss 49u IPv4 938605 0t0 UDP *:514
[root@localhost log]# ps -ef |grep 938605
root 17724 21799 0 16:49 pts/0 00:00:00 grep 938605
[root@localhost log]# ps -ef |grep 14524
zenoss 14524 1 0 14:24 ? 00:00:01 /opt/zenoss/bin/python /opt/zenoss/Products/ZenEvents/zensyslog.py --configfile /opt/zenoss/etc/zensyslog.conf --cycle --daemon --useFileDescriptor=15
root 17741 21799 0 16:50 pts/0 00:00:00 grep 14524