The symptom
The MacBook wouldn't turn on, no signs of life at all. When the MagSafe charger was plugged in, no LED lit up. Power draw was 5V 0.02A.
The diagnosis
Based on the measured value, the technician suspected a short circuit on one of the main power rails.
What was done
Using a multimeter in continuity mode, the PPBUS_AON line, which is the Mac's 12V rail, was tested to check for a short to ground. The technician's diagnosis was correct: this line was indeed shorted.
Current (1V 1A) was injected into the line to identify the faulty component.
A tantalum capacitor was heating up and was replaced, along with its two neighbors, which also showed signs of heat damage based on their appearance.
Result
After replacing the three tantalum capacitors, the short circuit on PPBUS_AON was gone. After reassembling the motherboard in the chassis, the Mac booted up fine and everything worked.
Another Mac repaired!