You may have a faulty router. Double check the cable from the modem into the router goes into the WAN port and the devices you want to connect go into the basic slots. Usually the WAN port is a different color so you do not mix up the ports.
If you still are having problems, try typing "ipconfig/all" into a computer connected to the router and paste the results.
Normally how this works, is the router gets all the information it needs from your modem (DNS, IP etc). And then your router works as a DHCP server and assigns connected devices a local gateway address, a private IP address and DNS servers. These three bits of information are essential to proper internet connectivity.