Diagnosis
Power supply circuit is dead. The external power brick is the most likely failure point.
How to Fix It
Unplug the power brick from the wall and monitor. Inspect the DC barrel connector cable for damage. Check the brick's LED indicator if it has one. Plug only the brick into the wall. If it shows no light or gets abnormally hot, it's faulty. You need a replacement 12V DC adapter with correct polarity, barrel size (typically 5.5x2.5mm), and at least 3A rating.
If That Didn't Work
The internal DC power input board or mainboard is faulty. This requires opening the monitor. Check for blown capacitors or burnt components on the small board where the DC barrel jack connects.
Heads Up
Never force a different power adapter plug. Incorrect voltage or reversed polarity will instantly damage the internal electronics.