Check the workstations using ipconfig /all and find out if the ip range is within the address range you assigned, if it is a different address then the workstation failed to contact the DHCP server and has gone into apipa mode. The Network Interface Card might be assigned an incorrect driver. Another possible cause of the problem is that the patch cable is not plugged into the Network Interface Card, or is not connected to a switch on the other end.
However, it could be that the server has run out of IP addresses that it can assign to clients. You can easily tell if this is the problem by comparing the size of the DHCP address scope to the number of devices on your network that request IP addresses from the DHCP server. But since only some of the workstations have got addresses the problem might be the DHCP server. Start off by doing some ping tests to verify that the DHCP server is able to communicate across the network.
If the DHCP server is able to communicate with other computers on the network, then I recommend verifying that the DHCP server has an IP address that is compatible with the scope that the server is configured to assign addresses from. The server itself has to be assigned a static address in the same subnet range, such as 192.168.0.199. If this still doesn’t solve the problem make sure that the DHCP server is still authorized by the Active Directory to lease IP addresses.
You should also check to verify that the scope is active, and that the necessary services are running on the DHCP server.
You will need to setup a primary DNS server in the larger branch office. Configure it as a primary forward lookup zone for the domain name of your company. Before you install DNS make sure your computer has a static ip address so it does not get one from the DHCP server. In the small branch setup a second DNS server. Configure it as a secondary forward lookup zone with the same domain name as the primary DNS server.