What I'd do

Turn off the legit DHCP device
Get an IP from the dodgy unit
Find out the manufacturer based on MAC address of the dodgy DHCP
Ping it
Break out the separate floor switches until the device disappears so you can narrow down the floor which you've done
Go door to door until you find it (assuming the ports coming in at the floor switches aren't labelled)
If you can't find it (locked room etc), just keep pinging it and unplugging individual ports at the floor switch until it stops responding. At least then just that port is disabled.

More likely it's a LAN port (not WAN) that's connected to your LAN. If it's an Airport perhaps it's set up to join a wireless network and provide that on the Airport Ethernet port. i.e. configured the wrong way around.

Could easily be an Airport Express too. It can bridge both ways.