Monitor does not come on when laptop is switched on

This issue could be due to presence of static charges on the notebook or hardware malfunction of the display screen or defective video card on the notebook. To isolate the exact cause of the issue, perform the following steps.

Step 1: Hard Reset

1. Unplug the AC adapter from the notebook PC and remove from any port replicator or docking station.
2. Remove the battery from the notebook battery compartment.
3. Press and hold down the power button for about 20 seconds.
4. Insert the battery and plug the AC adapter back into the notebook PC.
5. Press the power button to turn the notebook PC back on.

This will discharge the static charges from the notebook. Now check for the issue. If the issue persists, then connect an external monitor to the notebook and check for the issue on it.

Step 2: External Monitor

You can follow the steps below to connect an external monitor to the notebook.

1. Turn off the notebook.
2. Connect the monitor cable from the external monitor to the monitor port on the rear/side of the computer.
3. Connect the monitor to a power source and turn it on.
4. Press the Power button to turn on the computer.

At this time, please follow the instructions mentioned below for switching the display to the external monitor:

The notebook's video card supports three modes. Built-in screen only; external video only; and both on simultaneously (mirrored). If you're not seeing the image on the desired device(s), the notebook's video card is probably in another mode. Press FN + F4 to cycle through the display options: Notebook display, External monitor, both.

If you press FN + F4 once, the external monitor will display & there will be no Notebook LCD display.
If you press FN + F4 twice, the external monitor will display & there will be some shading on the Notebook LCD.
If you press FN + F4 thrice, both Notebook LCD & external monitor will display.

If the issue persists on the external monitor, then this could be due to defective video card on the notebook. However, if the display on the external monitor is fine, then the issue is with the LCD display panel of the notebook. In either cases, the notebook requires a detailed onsite diagnosis by a service technician.

If your notebook is covered under the HP warranty, then I would suggest you to contact HP to get the notebook repaired under warranty from HP.