There are various models of the HP 18. Assuming that the unit is not under Warranty or covered by any form of property insurance for electrical damage ... May I ask if your power cable was plugged into a Surge Protected power outlet or a Power Supply Unit of any kind during this power outage? Damage to electrical equipment may be covered by the manufacturer of electrical protection devices.
As you are probably aware, immediately prior to the lights going out, there is significant variation in the electricity being delivered to your outlets. If the Voltage or Amperage of your delivery exceeds the performance limitations of your power supply, this can damage the power supply, the DC input and any curcuit on the motherboard. Your motherboard appears to be a "TPV-Inventa Arroyo 3" with no onboard electrical protection.
You indicated that the unit turns on but the screen does not react. It is possible, but unlikely, that your screen is damaged and can be replaced. Much more likely is that the integrated graphics on the motherboard are damaged and the motherboard will need to be replaced.
This unit was released in 2013 so this is going to be a tough call. Computers become 10x more powerful every 5 years and Windows 7 has reached the end of it's service cycle. If you have a backup of your critical files, it's time to invest in a new unit. If you do not have a backup, consider pulling the harddrive and recovering your files. You could possibly attach a screen to a USB graphics output if it was absolutely necessary.
Thank you Sir,
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