ntoskrnl.exe BSOD even after reinstall

It is important information how this 16GB RAM is configured: Two 8GB sticks, Four 4GB sticks?.

If you test this RAM in your PC and Memtest throws up any errors, and your brother installs it in his computer and it throws up any errors then that is pretty strong evidence that one or more sticks of RAM are defective.

However, another important piece of information missing here is what you are using for a power supply (total wattage plus Amps on the 12v rail(s). And what you brother is using for a power supply.
Reason is that an under-powered motherboard can make good RAM bad.

Memtest works completely independently of any OS.
Linux may work through the errors, but if Windows won't then that is really not important.

Regarding the Video card:
That beeping you hear is important. It should be coming in a pattern, like Morse Code - a combination of short and long beeps. That code (ie: 3 long - pause - 3 long) means something.
It also helps to know the Brand and Version of the BIOS (Award, AMI, etc), because their beep codes are different.

Most modern motherboards will automatically disable the on-board/integrated GPU when it detects a dedicated card installed. But sometimes this does not happen. In these case it is necessary to go into BIOS and disable the integrated GPU manually.
Caution: If the dedicated card still does not work you will be stuck looking at a blank screen and no way to get back into BIOS to reset things! Be sure you know how to do a ClearCMOS or BIOS reset on the motherboard first!

Another thought is back to the power supply. Dedicated Video cards draw a lot of power compared to the other components in a system. If there is a problem with the power supply, or the system is underpowered to begin with, then adding the video card can tip it over into failure.
Under power could even affect RAM performance when the video card is installed.