Internet through modem works, but not through router

Your modem may be locked onto the MAC address of your computer.  You can try rebooting the modem while the router is plugged into the modem to see if the modem will migrate service to the router.  If that doesn't work, then try cloning the MAC address of your computer to the router.  You can do this by logging into the router and go the Router MAC Address setting.  Select either Use Computer MAC Address to automatically pick up the MAC address from your computer or Use This MAC Address and enter your computer's MAC address manually.  Click Apply to save the setting.  You may need to reboot the router before the change will take effect.  Test Internet connectivity.