Arduino powered from motor shield and USB issue
Looking at pictures of the Elegoo Mega 2560 they use a "hash fill" for the pour on the tab of the regulator, not a solid fill, and zero vias to another dissipation layer on the reverse. While this may look more funky it provides only a fraction of the heat dissipation of a solid double-layer fill, meaning the regulator is more likely to overheat. Also because this is a Chinese clone the component quality will be lower (cheaper) meaning the regulator probably doesn't have proper thermal overload protection.

So it gets too hot too easily, and pop your Arduino is dead as the regulator fails "short" and 12V gets pumped directly into the rest of your Arduino.

Byebye Arduino, and byebye computer (fortunately temporarily in the case of your computer).