Diagnosis
No power light means it's not getting any electricity. The internal power supply or a fuse is likely dead, or there's a break in the power cord connection.
How to Fix It
First, do the full circuit check. Unplug the power brick from the wall AND from the back of the monitor. Inspect the cord for any kinks, cuts, or damage. Firmly reconnect the DC barrel plug into the monitor's port—it can feel seated but not be. Try a different wall outlet without a power strip. Wait 30 seconds, then plug just the power brick into the wall. You should see a tiny LED on the brick itself light up (usually green). If that brick LED is off, the external power adapter is dead.
If That Didn't Work
If the brick's LED is on but the monitor is still dead, the internal DC board is probably faulty. There's no user-serviceable fix for this. Check your purchase date. ASUS offers a 3-year warranty for this model. Contact ASUS support with your serial number (on the sticker on the back) to start an RMA.
Heads Up
Never try to use a different power adapter unless you are 100% certain on the voltage (19V), amperage (at least 3.42A), polarity, and barrel jack size. Using the wrong one can fry the monitor permanently. Your best bet is to order an official ASUS replacement adapter.