If your router has a fixed IP, and it's the first IP in the range the DHCP server thinks it owns, then the first system asking for an IP will get the same IP as the router. I did this when connecting the router to the modem, and the modem and the router both wanted to be dhcp servers.

My solution was to allow the modem to provide DHCP in one subnet, which the router requests, and the router provides DHCP in a different subnet, which the computers request on.