Would it help if I took a physical picture of only the modem being plugged in and my network adapter status on-screen

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I can take you through the steps I took, as instructed by the agent.
1) Turn off machine, disconnect and power off modem, disconnect router
2) Turn on machine, wait 30 seconds
3) Connect and power on modem, plug in ethernet cable (note: coaxial cable is unplugged), power on modem
4) Check network adapter status (shame I have to reiterate this but Windows was set to DHCP), tell agent IP address (192.168.100.10), agent issues replacement modem
Now, even when the coaxial cable
was connected, the ready light would start flashing and sure enough it'd started using 192.168.100.10 again. Cycling the power would not immediately rectify this, indeed I waited over an hour and it hadn't fixed itself, only after I had been out for the entire day and come back was it working again. And it's been fine ever since I got back.