I purchased a .org domain from network solutions and I was thinking about using it for a intranet website running IIS6. I don't want this to be a public facing website. How would I set this up?
By my understanding, you didn't even need to purchase it. If the site is intranet, you could just set up a DNS server to point LAN computers from any domain to any server. On my LAN, I can point http://google.com to my file share.
In general you can point ANY host entry in a DNS configuration to ANY IP address.
Specific, you an do it unless your host blocks it (for example by checking it in an editor), but that is not a DNS intrinsic limitation (and one that is arguable - makes possibly sense "unless user overrides it" to avoid stupid mistakes by users with less knowledge.