Chosen Solution

iMac is dead. I tested the power supply separately from the logic board and all the pins match the expected amounts. When I attach it to the logic board, all the pins are dead, zero volts everywhere. Q: Does this mean there’s a short on the logic board? Wouldn’t the pins still show a voltage since the short is drawing power? Q: Do I need to supply voltage to the board to find the short?

Yes, you have a short within the logic board, often it’s the MXM GPU board that fails. Time to pullout the DVM and check the power rails for a short (without the power supply connected). You’ll need the board-views and schematics for the system.