Chosen Solution

I bought a replacement screen that included the home button and camera and that part works just fine but where the Home button ribbon meets the bottom half connection point, one of the prongs has broken off so only one of the contact points hits the cable, thus the home button doesn’t work. Does anyone know if this part of the phone is replaceable?

Yes it sure is replaceable. You have to replace the lightning connector using this guide. Good luck and be careful not to pry between the battery and the board at any time. Note: despite what the guide says, and if you’re careful enough, you do not have to remove the battery. So in my opinion you can try and skip steps 19 to 30.

I know I had this exact same problem because I broke the prong off myself but I fixed it like you said Rany and it still doesn’t work. (The Home Button)