MacBook booting to black screen
The fact that the back-light worked, but the display did not indicated the problem was with the display, not the logic board. Furthermore, the fact that I was able to project the display onto an external monitor validated that it was a connection issue between the board and the display.

I ordered a $10 USD LVDS cable, replaced it, and the computer now works :)

part in question:
https://www.amazon.com/Display-Cable-MacBook-Unibody-A1278/dp/B01N2T3CFD