DIAGNOSIS A flashing power LED usually means the monitor is stuck in a power cycle or isn't getting stable power. It's a protection state, not necessarily a dead unit.
FIX Do a full power reset. 1) Unplug the power cable from the back of the monitor. 2) Unplug the power brick from the wall outlet. 3) Also disconnect the video cable (HDMI/DP) from the monitor. 4) Wait a full 60 seconds. 5) Plug only the power cable back into the monitor and the wall. The LED should glow steady white. If it turns on, then reconnect your video cable.
IF THAT DIDN'T WORK Try a different power outlet and ensure you're using the original LG power adapter and cable. A different power brick might not supply the right voltage/amperage, even if the plug fits.
HEADS UP If the LED keeps flashing after a power reset with no cables attached, there might be an internal power supply issue, and you'd need to contact LG support.