Normally, the machine is not the direct interface to the internet (Public IP). How is the machine physically connected to the internet? Is there only 1 NIC card and Is it coming directly from the ISP or possibly via a 1 to 1 NAT?
What did you specify as an internal IP on 3CX or what does it point to and if pinged what return do you get? How are other devices in your network accessing the internet?
The system has some settings in the advanced parameters that were used to validate that the system was assigned a private IP according to the RFC. I believe this was to aid in the set-up of various aspects of the system and its associated header generation to the internal phones.
Assuming that you can get around whatever obstacles that arise with the system setup and operation, and that the system is working (meaning all system extensions and services, then you could use a private IP on the phones and use the same settings, other than the unique IP that each is assigned, as on your internal computers. The big issue is that all the traffic between the phones and provisioning, etc. will have to go out and then back in to hit the only available IP that sits with 3CX. The phones will be set as though they are external/remote phones.
I do not know if this is a supported configuration (have doubts) or really possible as I have never tried. I assume that there must be some firewall issue that is interfering with a conventional/normal set-up. If so, then perhaps posting that issue may result in some suggestions on how to resolve or at the very least putting the system into a DMZ might be an alternative.
