One of the key thing need to check is whether DNS name resolution working properly. This can be do by using Nslookup command line tool and type the name of the server or any of the DNS clients name which should be resolved to corresponding name. This should check in both DHCP and DNS servers, if they are in separate systems.
If you are finding any problem in this, check the network connectivity. Check the DNS Zone records for duplicate name or IP address.
Verify that the DHCP server had authorized in AD. Without DHCP authorization in AD, a DHCP server cannot do IP address leasing to client.
Try this probably it should work.