I just wiped the dust off my monitor (a Samsung T260), using the supplied cleaning cloth. I even read the instructions and kept within the limits of spraying my cloth with water 4-6 times. When I sat down again, the monitor was off. I pressed the “Source” button a couple of times to cycle through the available inputs, hoping to find either the laptop or the desktop, both connected to the monitor. No reaction. I pressed all the other buttons, nothing either. I disconnected and reconnected power. I checked that the power cable hadn’t magically unplugged itself and the inputs were still firmly attached. I started looking for a power switch in all the usual and unusual places, but failed. Defeated, I turned to the laptop and downloaded the monitor’s manual, only to find the obvious explanation:

There is a power “switch”, but it’s a touch sensitive area on the front side of the monitor (in contrast to all the other buttons, which are physical buttons hidden on the side of the monitor). It’s even marked with the universal “power” sign, but it’s quite easy to misread that as a label for the power LED that’s located a couple of millimeters below. But yeah, fine monitor. And it’s probably obvious to members of the iPhone generation.