Can you see if this issue is fixed by switching the power adapter from one of your two working monitors with the one that is having the issue?
I would rather buy a replacement adapter than deal with Asus warranty.
I have put the faulty adapter on the other monitors still turns them on its 100 percent the adapter
I have also had this same issue. For a while my monitor would randomly switch itself on; it then stopped doing that and would refuse to turn on unless I unplugged the power brick, wait for a minute then plug it back in.
Eventually it stopped working altogether. I RMA'd the power brick with Asus and a week later they sent me a new one (they didn't ask for the old one back, they just sent out a new one).
I got the replacement yesterday and my monitor is now working perfectly again.
Let's hope that Asus sort out these power supplies as I really don't want to keep RMA'ing one every 6 months.
I have the ROG SWIFT PG248Q and i also suffer from it switching ON by its self.
do you think this AC Adapter would be compatible with my display : http://www.ebay.com/itm/121828159363