DIAGNOSIS The monitor is powered on but not receiving a video signal from your PC. The most common cause is the monitor defaulting to a source or refresh rate your GPU can't initially output.
FIX First, power cycle the entire chain. Turn the monitor off with its power button. Shut down your PC completely. Disconnect the DisplayPort or HDMI cable from both the monitor and the GPU for 30 seconds. Reconnect firmly, ensuring the cable is fully seated. Power on the PC, wait 30 seconds for it to fully boot, then turn the monitor on. Use the monitor's joystick to manually open the input list and select the correct port (DisplayPort 1, DisplayPort 2, or HDMI).
IF THAT DIDN'T WORK Your GPU may be trying to output a refresh rate or resolution beyond the monitor's initial capability. Boot your PC with the old monitor. In Windows Display Settings or NVIDIA/AMD Control Panel, set the resolution to 2560x1440 and the refresh rate to 60Hz. Shut down, reconnect the LG monitor, and boot. Once you have a signal, you can increase the refresh rate to 144Hz or 180Hz (Overclock) in the OSD under Game Adjust > Overclock.
HEADS UP If using DisplayPort, ensure you are not using an old or faulty DP cable. Version 1.4 is required for full bandwidth. The monitor's "Deep Sleep" mode in energy settings can also cause slow wake-up; you can disable it in the OSD under General > Energy Saving.