If you’re ever trying to get dhcp to work in Linux, and the package you installed also installed a service file named dhcp at /etc/init.d/dhcp, ignore it.
You start the service not by invoking that script (which will apparently fail every time); you do so by running /usr/bin/dhcpd. Why? I don’t have any earthly idea.
Anyway, I hope to spare someone this anguish that I now know far too well. Skip the silliness and just start dhcpd.