DNS issues

WordPress is installed and sorking properly at my client’s IP address. They have purchased a domain name that they want to use aas their permanent address. When I attempted to change the URLs in WP, no pages loaded and I got a “page not found”. I then had to go into the database to change the values back.

What exactly do I need to do to fix this problem? What would cause WP to behave this way?

Here’s a bonus… Whois records show that the domain is registered with Melbourne IT, however Melbourne IT shows no records of my client’s domain…