I had two cases in a row recently of many-layer power-planed boards with power supplies that wouldn't come up above a diode drop, and I was able to use a trick devised for the first one to solve the problem on the second one, too --
I set a current-limited supply to ~30mA & left the board to stabilize thermally. I then looked for the 'hot' parts with an IR thermometer. Worked like a charm.
Temp. rise was about 1oC @ 20mW. The IR thermometer? $14 well-spent.
Cheers, James Arthur