You have migrated your DHCP role to a different server. For example, from a Windows 2003 to a 2008 server and you have reconfigured the DNS entries so clients are issued with new DNS server addresses.
You have disabled the scopes on the old DHCP server and unauthorised the server as a DHCP server.
You find that your clients are being assigned ip addresses from the new DHCP server but the DNS entries are still set to the old ones.
This is an odd fix, but you will find that disabling the DHCP service or uninstalling DHCP from the old server, will resolve the issue.
Disable the DHCP server service from the old DHCP server and let us know how you get on with this fix by commenting below