You don't say whether the PCB is populated or not, but assuming not.
Set a bench PSU in current current limit mode to as high a current as you sensibly can (somewhere around the expected circuit current consumption or higher) and put it across VCC and GND. Then go around with a DMM (hopefully a 4 1/2 or 5 1/2 digit) on its most sensitive mV range and work across the board, starting at the inputs and measure the voltage between VCC and GND points. The lower the mV (maybe 10s of uV) reading, the closer you are to the short. This can actually be a pretty sensitive method.
If the PCB is populated, it's pretty much the same as above, but set the PSU to less than the normal VCC rail voltage before going into current limit mode.