The DHCP on your router isn't working properly. You should perform a hard reset on the router by finding the reset button on it. Take a pen or other small pointy object find find a tiny hole on the router. Press and hold this for 20-30 seconds. This will reset to factory settings and the password to the router will also be reset to its normal default.
Reconfigure the router as if you had just bought it new and it should work properly this time
This is from a DI-624 Router, and should be very similar to yours: