Maybe you're already working this angle, but it's not clear in your question. Is your DNS server registered with the NIC, or with a registered top-level DNS server? Did your ISP/WAN provider give you any DNS server addresses to link to your server?
If you do a name search and your DNS server doesn't have the information, it goes to other DNS servers it knows about. If those servers don't know, they query still other servers, and so on until one of them has the information and it gets handed along back to the client. Your DNS then caches the data for a period of time in case other clients request that data. That's a simplification, but the point is that your DNS has to talk to other DNS servers to do its job, because it can't store every name lookup your clients might want to use.
Your ISP/WAN provider, whoever is selling you your internet connection, should be giving you some DNS server addresses that your DNS can query.
Good fortune,
Don