As others have stated, your answer may not lie with DHCP, and definitely not "solely" with DHCP. DHCP was not designed with nor intended for the task of deciding which devices may or may not gain leases, and I don't blame you for not wanting to manage MAC addy's of a 100-node network. Though ... nice technique OB, and he's right, OB's technique would not take too long to implement nor maintain on a 100-node network. I just want to expand on Arsynic's explanation as I think the answer was very thorough but may have been overlooked.
Getting back to the discussion about physical access -- you stated that this employee plugged his/her personal laptop into a spare LAN jack in the department. Why is the unused jack even patched into a switch in the distro closet? This is only one of several reasons why unused jacks simply should not be patched into distribution, i.e. jacks should only be patched into distro if they are allocated to an active piece of production equipment. At the distro closet(s), remove the patch cables for all jacks that do not have active production equipment plugged into them.
You've mentioned that this employee was reprimanded, indicating you have policy and support of management. That's step 2 as Arsynic stated. Good! With respect to IT policy, add the review of DHCP leases to IT policy -- if you have specific naming conventions for your production equipment, it's easy to spot a DHCP lease to "Johnny's IPOD" or "My Laptop" and investigate.
Lastly, IF an employee is inclined to circumvent the above 2 levels, i.e. physical access and policy, and manages to connect his/her personal equipment, without managed switches that CG commnented about the rogue equipment will gain a DHCP lease. If you have a Windows AD, internal resources are generally protected by domain authentication, and proper audit settings and review of security logs (and DHCP leases stated above) can flag a breach to internal resources. External resources, i.e. internet access, etc. may be protected by a decent edge device. A properly configured internet gateway or threat management gateway (TMG) will deny access of an unauthorized device on the network. Given the protection and blocking of access to internal and external resources, the fact that a rogue piece of equipment may gain a DHCP lease becomes a non-issue.
--C