I tried the suggested Microsoft reboot method (in this case unplugging it for 30 seconds, then plugging it back in). No luck. It was still dead.
I called Verizon on Tuesday to make an appointment for someone to come out and replace my dead unit, and the automated system told me I had a DVR that needs to be replaced, and asked me if I wanted to be sent a new one. Well, yes! That was nice that it already knew I had an problem, and offered a suggestion to resolve my problem. I never had such swift customer service from anyone at Brighthouse! It was always half an hour of my trying to convince a very bored-sounding person that I had tried everything, and that my DVR was indeed dead.