DIAGNOSIS You've got a dead monitor, no life signs. This is almost always the internal power board giving up, and it's a known weak point on this model. The external power brick is usually fine, it's the component inside that fries.
FIX You're looking at a board replacement. Open the monitor case (plastic pry tools help), locate the small internal power supply board, note the model number, and search for a replacement online. It's a standard procedure: unplug the few connectors, unscrew the board, swap in the new one. No soldering needed, but you need to be comfortable opening electronics.
IF THAT DIDN'T WORK If you're certain the power brick is outputting the correct 19V, then the main logic board might also be dead, but that's rarer. A full board set replacement is the next step, but at that point, weigh the cost against a new monitor.
HEADS UP Be extremely gentle with the thin ribbon cables connecting the control buttons and the panel itself when you're inside. They're fragile and a pain to reseat properly.