There is no internet connectivity with the modem and router together, however, eliminating the router and just using the modem works fine. There doesn’t seem to be a power issue with the router.
What could the problem be?
Router won’t work with modem
May we know what is the brand of router and modems are you using? When you connect the router to the modem, you check and verify if you are able to access the router’s GUI (usually is 192.168.1.1 with user name left blank and password set as admin). You should set up the SSID and passkey properly.
You may also try to update your router or reset it. That would refresh its setting which most likely is still not seeing the new modem.
If the steps above did not help you, you may need to contact your service provider. They may need to update your router information with the modem details to allow connectivity.