The DC cable is perfectly fine. The solder pads that the DC cable connect to, as well as neighboring solder pads, all show the proper ~20V.
Anyway, I'm pretty sure I found the culprit. There's a few SMD components that look like they're done for, and they're all in the power circuit (labeled with a P before their label).
New question, is there a way to wire an AC adapter directly to the battery prongs on the motherboard? Of course I'd have to match the battery voltage and current, but that's what I was thinking as a possible solution.