Thanks for the suggestion. I did get them involved (their tech spent 3 hours on the phone with me looking at screen sharing sessions on 3 PCs as we tried to tweak Zone Alarm to work with the software). We were able to get one of our PCs running ZASS 70_470 to let the software run after some combination of opening ports, adding IP addresses to the trusted zone, and adding a few of the application's dlls to the trusted programs list. I then tried to downgrade the other 2 computers from 70_473 to 70_470 but was unable to replicate the settings (and some of the settings for the trusted dlls that Zone Alarm accepted on the working machine it would simply not accept on the other PC's).
I am going to try the suggestions to look at Zone Alarm's log to see what it is doing, but am offsite until Thursday and Zone Alarm will not let me change any of its configuration settings or see the log remotely, even after editing the disableKeyboardMouseProtection setting in the XML file that some people suggested (we made the change but I am still locked out, using a version of UltraVNC).
Still no follow up from tech support from the paid phone call, and have emailed them as well, but have gotten nothing back other than a "maybe you'll hear from us in 2 business days" response.
If I don't hear back from tech support and if my attempts to get things working based on the log entries don't lead to anything, I guess we'll find out what happens when I ask for a refund...