It took one evening but I fixed my HP laptop hinges
with baking soda and superglue. Also relaxed the hinges a little so now it actually opens with one hand (and hopefully doesn't break again very soon). There is also spare display lid on Aliexpress costing about $35, since everything else seems okay maybe I will buy it if anything else breaks. Some photos of the problem and fixing process follow below.
These tiny screws and nuts surrounded with thin plastic are supposed to withstand the force required to open/close 15.6" display lid. It doesn't seem much but if you try to turn hinge with your fingers it is easily 5-6 kilo of effort. I barely could turn it using my pinky finger. Huge display creates a lot of leverage.
Baking soda and superglue when mixed create instant and very strong polymer with very strong adhesion to almost everything except polyethylene. Unlike epoxy which takes time to harden this happens instantly (and also releases some poisonous vapors in the process so ventilation won't hurt). It doesn't stick well to anything covered with oil so WD-40 (or any oil) could be used to prevent it and help clean your hands. After it polymerizes it remains a bit soft for very short time and can be cut with knife to shape it a bit. Having a pet nearby is also important because their presence has therapeutic effect and prevents you from throwing and breaking stuff in frustration when something goes wrong - you would be ashamed to do it in front of your dog, right? Right.
Remove most of broken plastic because you want to put as much compound there as possible. Remove any dirt. Protect places you don't want to get superglue into. Since we are gluing in a nut we protect the treads by screwing in a lubricated bolt - the glue won't stick to it. I positioned it in the right place and fixed it with a little superglue so it doesn't move. Then put a little baking soda around it and add a drop of superglue. It turns into hard plastic instantly! Then add some more soda until there is no liquid glue visible. Blow it off. Cut unwanted extras and repeat. Done.
I also added some around nuts still in place - because they WILL break at some point.
Other side is trickier - it has some cables running between these nuts. Also nuts here are completely demolished. No, the laptop wasn't dropped. It spent three months next to my couch where the lid was opened about four times per day. What sort of crap they make this plastic of?
Anyway it will be hard to cut the canal for cables later and I want to mold the nuts in place using as much compound as possible to I use chewing gum (yuck!) as a placeholder. Then repeat previous steps. After nuts are done. chewing gum is cut out with a knife. Looks ugly but it works.
Now polish them a bit with sandpaper and assemble the display back. It works! Let's see how long it lasts.
As you can see, HP could easily make these parts more robust. Just a little more plastic around, longer screws, not so overtightened hinges. It is definitely by design.
I can say one good thing about HP though. Their service manual is pretty clear, also all screws are marked on the actual parts so just by looking at the part you can say which screw goes where. They even put V and X marks on every hole which tell you if you should screw something in it or not. There are only three kinds of screws used to do this repair (take off the bottom lid, display lid and hinges). All cables are marked in correct orientation and order so you won't even try to insert display cable upside down. It is not too bad when it comes to serviceability.
But it is unlikely that I am going to buy another budget HP again unless they fix their shit. It used to be better. Now it reminds me of cheap Acer laptops back in the day when all Acers were cheap crap.