|It's possible that the authoritative server is in-house. That was certainly how we ran things where I used to work.|
But, from what I have read in this thread, I strongly suspect that you are correct. All that is needed is an A record in the ISP's DNS server. This assumes that the internal server has a routable address and that the virtual NIC is configured correctly.
If this is a commercial setup I would really advise the OP to get a professional in to help; he doesn't appear to have a grasp the basics of IP networking, so I suspect there may be other concerns.