hp 840 g3 only has the integrated HD graphics (within CPU) so its pretty rare it goes bad. If you remove all ram and boot with only cpu you should get beep/blink codes for missing ram that means motherboard is "most likely" fine. Does not still mean there can be problem with it.
With HP laptops failure is 80% the gpu chip, that was the case atleast 5-10 years ago this might of changed. Ive had the 1 blink been multiple different things, from corrupted bios, bad bios chip, dying northbridge and gpu chip etc.
You can try to recover bios with Windows + B key at startup, follow this guide, If you cant get into bios recovery mode with it (might be different key combination too) then even the USB method wont work, just try the recovery mode without usb stick first, then do the steps below this then come back to this video and try the USB method if needed:
View: https://www.youtube.com/watch?v=OkadkPyGjY4
Like previous poster said always go for warranty first, if its OUT of warranty then you can try the basic. Check for broken USB ports on the laptop, looking for shorted pins (always remove power cable when removing or touching anything, also first thing to do is remove main battery from the laptop) seen at 2min40sec on below video
View: https://www.youtube.com/watch?v=M9c7w77tS3I
- remove main battery and power cable, press power button for 30sec-1min continuously, plugin ONLy power cable and try to boot. If it boots without battery then battery is bad.
- if that doesnt work you can see the small cmos coin battery on the right (covered with black tape) , remove the white ribbon cable connector carefully which connects it to motherboard. wait for 10minutes and plugin the cmos batery back and try to boot.
Next is obviously take it apart until basics left (with non conductive surface), motherboard , ram , cpu, power cable. Nothing else, then plugin power cable and see if you get beep/flash codes, if no monitor cable is connected you obviously cant see picture anywhere. If it boots like this then problem is somewhere on the way like shorted LCD screen / connector, or wifi card , whateevr can be the cause. If it works barebone then find the cause by slowly adding things back and testing in between, make sure to always use non conductive surface and remove power cable between attempts, and obvioysly main battery need to be disconnected at all times.