upgrade to a different model ;).....kinda serious. the 278 is a great model and a similar board and firmware is used in a bunch of similar models so the issue you are having is most likely related directly to your physical model. Have you had your monitor swapped out before, or have you just had the PSU replaced?

Depending on the issue the previous power Supply had could have caused some issues with the monitor itself. Before we jump to conclusions though, It is highly unlikely that the PSU going bad caused an issue unless the cause was a power surge of some sort that the PSU could not protect the monitor from. If you have issues from the start of getting the new PSU then it is related to receiving the new PSU. If the issues exists before the new PSU then it is mostlikely related to the monitor itself. As for it turning on in the middle of the night I would think the first thing is do you have any animals in the house that like to touch things because that happens. Also it could have been a unikely chance of moisture getting into the button and causing a false hit on the power button. Another thing you could test is to turn off your monitor then unplug it from the wall for about 10 seconds and plug it back in. This simulates a power outage. After plugging it back in did the monitor default to the On position or did it remain powered off?

Try and duplicate the issues multiple times so that you can find the cause and either call up asus to find a solution or maybe just find out its just an extra feature of the monitor.