OK. I admit that it was me, but I stumbled over the power cord and disconnected the power to one of our computers - a fairly old one, but it's still useful. It was on at the time, so of course the disconnection meant that it stopped operating.
Within seconds, I had reconnected the power, expecting the computer to go through a series of checks as they do when they start up following unexpected close downs. But --- nothing, just the noise of the fan, one little light and an intermittent "beep". I tried several times, but, no, nothing except the same beep.
A little googling, and the answer was there: if there's a problem so early in the start up process that the computer can't display anything on the screen, it communicates by beeping. A single beep means "memory chip refresh failure". The advice about what to do wasn't so clear, however. So throwing caution to the wind, I picked on what seemed to be the simplest answer which was to "reseat the memory chip or to replace it". Replacing it was out of the question, as I don't have a drawer of old memory chips. Reseating it, however, was a possibility, at least, if I could work out what had to be "reseated"! So after further googling so that I could actually identify the relevant bit inside the computer, I undid the screws, changed the memory chips around, put everything back together and held my breath after I turned the power back on. For once, fortune was with me, and after a number of self-checks, the computer was back in business. Big sigh of relief!
How it is that a power outage affected a memory chip in this manner, I don't know, but I don't want to repeat the experience and I am certainly now keeping out of the way of the power leads.