Does the monitor display the ASUS logo or other information for a few seconds when you first press its power button to turn it on?
It should do so whether or not it is connected via a cable to any video source.
If it doesn't do that then it is likely the source of the problem is the display itself, or IF the display uses a separate power "brick", then that is suspect as well. You could initially check that with a voltmeter and ensure it is putting out the voltage the display label says it requires.
If it's "stuck" in what appears to be a loop of cycling un-corrupted screens of various colors or patterns, then it is in some sort of self-diagnostic mode.
This may be due to a problem with the button/switch assembly. I've run into that problem on Acer monitors. It suggests that at least one button is "stuck".
The self-diagnostics mode on some displays is started by pushing and holding one or more of the buttons just before and hold it as you power-on the display. Sometimes the diagnostic is invoked by using the buttons but requires removal and replugging of the power cord.
It could be another reason, as it's possible the buttons on the ASUS do NOT do anything at power-up, but the self-diagnostics could be due to a failed part or debris inside the display.
You might try using compressed air to "blow-out" dust from the interior of the display (if vents make that possible).
You might also try putting the display in a very cool room, letting it acclimate, then powering it up to see if temperature makes a difference.
Same for a very warm room.
If the symptoms change, it suggests a failed component or a poor connection that is temperature sensitive inside the display.