Internet access directly through modem, but not through router [duplicate]

Had the new house wired up with Xfinity this morning. Cable guy was here for just over an hour. Modem was registered and hooked up. He plugged it into my PC directly, and the Internet was working very quickly and reliably, with speeds as advertised.

When he left I proceeded to disconnect the modem from the computer, and add the router to the setup. The router is verified working, I’ve been using it as recently as Saturday on the DHL connection back home. Though the wireless network activates and is strong, and appears to connect to the Internet, webpages will not load. Wired connections through the router show the following error:

Windows troubleshooting yields the error message

The remote device or resource won't accept the connection.

I did some research on that error message, and got a lot of minor problems with quick solutions, the most popular being disabling proxy settings, that did not help me. So I moved on to search terms like "Internet through modem not router." This brought up more complicated answers having to do with the modem grabbing the MAC address of the computer instead of the router, or not being able to grab a router address at all. This sounded logical to me so I did some playing with it.

All several times and in different orders, with no luck.

In short, all devices are working, I have internet to the modem, and communication is strong to the router, but no internet access wired or wirelessly.

Not sure where to go from here. Got any ideas?

UPDATE: Here is some additional information.

When I switch from using the modem for connection back to trying the router, I get a network error window stating:

Windows has detected an IP address conflict. Another computer on this network has the same IP address as this computer.

When running the ipconfig while pulling Internet directly from the modem, I get 4 results under DNS Servers:

2001:558:feed::2 2001:558:feed::1 162.150.21.49 162.150.8.49 

When running the ipconfig while connected to the router, only one DNS server is listed:

192.168.1.1