You need to clean up the attributes of the old domain controller in AD (see: How to remove data in Active Directory after an unsuccessful domain controller demotion). Perform these steps even if the domain controller was demoted successfully to verify that all of its attributes in AD have been removed. The server also needs to be deregistered in DNS forward and reverse lookup zones and WINS as well. When these steps have been completed, allow time for all of the changes to replicate throughout AD, DNS and WINS after which you can introduce the new domain controller with the same IP address.
Though the solution above meets your immediate needs, going forward, I recommend that you implement DHCP to prevent from having to touch each workstation manually to accommodate changes to the network infrastructure. This would prevent the need to use the same IP address by changing the scope options after which each workstation would need to have its DHCP lease renewed or simply be restarted to take effect. It is not recommended that servers use DHCP, so they would still need to be updated manually or administratively using a script.