Just to confirm, the RAM you're using now is the original that came with the laptop, yes?
If so, there shouldn't be any kind of compatibility issues, unless you bought it refurbished or used or otherwise.
The hardware allocation issue is usually one of 3 things, the most common being the iGPU eating it up (but we confirmed that wasn't it, or at least the BIOS wasn't set that way apparently), the second is incompatible RAM, the third is faulty DIMM slots.
It's possible that the 8GB stick you tried was also incompatible with the mobo, the best I could recommend is looking around the service manual that usually comes with your laptop, see if it lists what speed and type of RAM it uses and compare it with each stick.
The first thing I would suggest is booting into a live Linux distro and see if it shows the same, and testing with both the 8GB stick and the 2x2GB. If it's the same, then we can confirm it's either a BIOS or a hardware problem and if it isn't we can confirm it's just a bad Windows install, and you can try doing a clean reinstall (or, if you really don't want to unless you're sure, try booting into a live Windows install and confirming before the clean install). If it's the same with the Linux distro, try clearing the CMOS, updating the BIOS, then resetting the iGPU allocation, boot back into the Linux distro and check. Still the same, we can confirm it's either incompatible RAM or bad DIMM slots.
The best way to test that would be to simply buy a couple sticks of RAM you know should be compatible based on what's in the service manual, and seeing if they work. They do, great, just incompatible RAM, if not, faulty DIMM slots, not so great and I would suggest either getting it replaced by whoever you bought it from or using the warranty and seeing if HP will replace it. Before you try buying, you could also try contacting HP and seeing if they'll just send replacement RAM free of charge, but I'd imagine they'd probably just request you send the laptop in anyways.