When I remove all blue jumpers and test continuity between ground and each pin, I get nothing.

But even on an already working unit, that's the case. I assume this is because some sort of power relay which is tripped (not sure).

I can only obtain connectivity if I test between the top-right and bottom-right pins (see exagerated diagram below). Even on the working unit. I can't get continuity by touching ground and any pin -- only when I touch the top-right/bottom-right.

And no continuity between top-left and top-right with all jumpers removed.

On the bad unit, I don't get power on the 5V "rail" on either blue jumper. On the working unit, I do.

Jumper Diagram ('---' character indicates a blue jumper)

O---O
O---O