Fortunately, Richard is a genius and can do tech support on the phone. He suggested that maybe the battery was loose, as that had been the problem when he bought this machine. It didn't seem very loose to me, but I took it off and put it back on again, and then it started working.
For future reference, when the battery light flashes very quickly at a constant frequency, it means there is a fault with the battery. When it's charging, it normally flashes twice, then a pause, then twice, then a pause.
Current temperature of the h-l: 37.6 degrees C, 2 hours after taking paracetamol (acetaminophen). Current state: nauseous. Am wondering whether this is some sort of gall bladder woe, as the symptoms I have seem to be almost entirely digestive. Gah.