Note: I'm offering this self-answered question hoping it will spare others similar troubles. I don't know what other Netgear router models are affected.
The Comcast/Xfinity cable modem itself has Internet connectivity (verifiable via a direct-to-a-computer Ethernet connection) and - if the modem isn't just a modem but also has a Wifi router built in (residential gateway) - it must be in bridge mode.
The cable modem has been power-cycled and given enough time to come online before you've connected the router to it by Ethernet cable. When in doubt, power-cycle both devices and do not reconnect the router until the cable modem is back online.
The router never manages to connect to the Internet via the cable modem - the Internet-connectivity LED on the device remains orange (white is what indicates an established connection)
The router's web-based administration application at http://192.168.1.1 tries to connect, fails, offers to try again, and keeps failing.