UPDATE! We swapped out the HDMI cable and were able to get into the game. Got onto our Wifi network and an update installed automatically. After that, on a hunch, we shut down, put the supplied green HDMI cable back in place, and started up again. Presto! Everything's now working great!
Maybe the cable had been somehow kinked before. I did change the direction of the cable when reinstalling (swapping which end goes into the pi); dunno if that made a difference, but something did.