Exchange sending but not accepting email - mail acceptance failure

I have a newly installed Exchange 2003 Server Standard running on Windows 2003 Server Enterprise. I have correctly set the MX records with the domain host, and correctly configured the firewall to forward port 25 to the Exchange Server. Our ISP is not blocking the mail. I am able to send mail outbound, which is immediately received by outside parties, but no mail will come inbound. I first attempted to configure things manually, and then tried to reset things to the default and run the internet mail wizard, but the results are the same. I installed the Microsoft Exchange Troubleshooter (ExTRA), and ran a mailflow analysis, which complained of a 'mail acceptance failure' (if you google that phrase, you get the technet article). The gist of it seems to be that my server's name and the name of the DNS domain that I want to host mail for are not the same. The complaint is that the FQDN and the DNS resolved names are not the same, which is true. I always understood that it was not good to do that, and in fact I have an SBS server using just such a configuration, where the server name and domain name are different, which is working fine.

I tried to resolve this by adding a forward zone to the DNS server with the same name as the mail domain, but that didn't do it.

I need to understand how to get mail flowing inbound.