Solved; and this is clearer than viewtopic.php?f=2&t=1178
Twice I started my laptop with plug-in power but with the battery critically low from prior use, which had left me with roughly 5 minutes of power by the time I started shutting down, on a computer that usually claims nearly twice as much time on the full battery as I actually get in practice. After AC bootup, pressing F1 to bypass the warning got me a blank display. Rebooting didn't help.
Solution: Pull the battery out physically. Boot cold. Within minutes, put the battery back in. Once, I put it back in after I had logged into the Linux OS but before I logged into my Linux user account, which is only moments after booting up. I don't know whether the battery can go back in earlier, but it apparently can.
Later, I had let the battery run down until the computer stopped working, and cold-booting with the battery in place failed to produce a bootup. But, apparently, yanking, cold-booting, and pushing the battery back in before the setup login works; if so, waiting until the hard drive login or the Linux OS login is not necessary. However, in between I had tried the procedure with waiting till after the OS login before pushing the battery back in, after which the screen froze and I powered down without shutting down, so this test wasn't perfect. But it appears that we can push the battery in just seconds after AC power is up and a normal display is beginning.
Computer: Dell Latitude C840. Yes, that one.