Which DHCP server is it? Is it ISC's dhcpd? If so there should be a dhcpd.conf file somewhere, depending on your distro, with configurable parameters in there that you can change. And I think dhclient.conf is the file that you actually use to id specific MAC addresses. Otherwise, find out which dhcpd is running and read its documentation. While the current set up you have is good in a security sense, it should be possible for you to change the policy to allow anyone to get an IP on the network.

You might want to find out why the previous admin limited the assignment of IPs thus, there could have been a good reason.