Just to close the loop on this thread (in case anyone else has a similar problem), I did get a replacement battery from Niterider. Followed the video on battery replacement on their website (though why they felt it necessary to create a video for something that could have been explained in a few paragraphs of written instructions I don't know). Turned it on, and . . . nothing. Same problem.
I sent them an email asking if they had any ideas of what else it could be. I got an email back a day or two later, asking me to call their tech support. I described my problem to tech support, and he asked why I replaced the battery, so I threw you all under the bus . . . nah, just kidding. He said it sounded like it was a bad switch, and that it would be a warranty repair. I told him I'd had the unit for more than a year, and I didn't know where my receipt was. He didn't seem to care. He said they have two-year warranties anyway, and just gave me an RMA number. He told me to leave the new battery in and they'd test the repaired unit with the new battery to double check that the battery is good and everything is working correctly. Sent it in and a week or two later I got the repaired unit in the mail. It's been working great ever since, and I now have a backup battery on hand, if anything else goes wrong.
I was all ready to ditch the Lumina and buy something else, but Niterider customer service came through for me, again (when I needed a couple of extra mounting brackets for my NR Solas taillights, they sent two out to me - no charge). I'm having a real hard time coming up with something about them for which to complain.
KB