Main board heated bed connectors aren't powering up
Considering:


  Multimeter shows zero across the board's heat bed contacts


this implies that 


If you measured resistance, the heated bed has no resistance. Basically this implies that the bed has a short. This might be the reason why it is not working. If you would power it as such you create a short. Instead of replacing the board, you need to replace the heated bed. Typical values for a heated bed of about 200&nbsp;x&nbsp;200&nbsp;mm are in the order of 1.2&nbsp;&Omega; (measurements between 0.9 and 1.5&nbsp;&Omega; are reasonable to be expected).
If you measured voltage, the heated bed does not receive power for heating, or the power does not reach the bed (not turned on or broken wire?). It would then be wise to measure the resistance (of the bed and the wires). If the resistance is in the order of about 1.2&nbsp;&Omega; (see above) for the bed, you could try to connect the heated bed directly to the PSU to see if it gets warm, if so, please disconnect immediately to prevent damage. From this experiment you can find whether the heated bed is broken (or the cables), or that the board is not functioning correctly, this is, however, strange as you tried 2 boards. A possible suspect could be the MOSFET that schedules the powering of the heated bed if you use an external MOSFET board that it.
If you measured current, then you found out that no power is delivered to the board, but you also might have broken your board in the process, as measuring current is a (close to) 0&nbsp;&Omega; connection and has to be done in line of a circuit.