|Are you sure the laptop is using the Windows server as its DNS server and not, for example, your router? Is it set up with a manual IP address or does it use DHCP? If the latter, where is your DHCP server - the Windows Server or your router?|
No, you don't have to buy an IP address (assuming this is a private network). Just use one of the private address ranges - 192.168.1.0/24 is as good as any.