If there seems to be a power on issue, the power system is the best suspect. There is no easy to spot & replace battery. You can take the one cover on the rear off and there is a black space on the right that is the battery. No way to see how it comes out.
You can follow the battery steps in this guide to remove the battery. There are 3 hidden screws which keep the battery in place. You'll need a #2 star bit to remove the screws once you take the black stickers off the 3 screw heads. The iFixit 54 Bit Driver Kit has the bit you need.
The battery is a model HP LR08XL. It isn't common so it is a bit more expensive than some other batteries. You can use your favorite online shop or search engine to find a replacement using the model number. Amazon in the US has them.
Note: many manufacturers appear to be in your country but actually ship product from China. Look to see where the company says it will ship from if you care about local stock vs., in-country vs. Chinese. The further away, the longer it takes to arrive most often.
Install the battery and button the laptop back up. Charge for several hours before first use.
I found that my laptop was not charging the battery properly while I was using it, only charging while off. I suspect the power brick.
I do believe the battery was faulty, not sure about the power brick.
With the battery removed, you cannot use the laptop on AC power only. Oh well, thanks HP.
Hopefully someone with this laptop or similar finds this helpful.