Sounds like it could be either a cracked solder joint around where the DC in socket is soldered to the circuit board, or it could be a bad connection somewhere, or maybe the plugpack adaptor isn't supplying enough current, you can check for cracked solder joints by using a strong magnifier to inspect the solder joints.
Sometimes those circuit board mounted DC in sockets can go bad and develop bad contacts, if the Boss ME-30 is powering up via batteries okay, that suggests to me that the small switch contacts in the DC in socket are okay, the small switch contacts disconnect the batteries when you plug in the plugpack adaptor.
You can check to see if power from the plugpack is getting to the rest of the circuitry of the Boss ME-30 by using a multimeter set to read DC volts, touch the black probe tip to a suitable ground-point on the circuit board and try touching the red probe tip to the solder joints of the DC in socket on the circuit board.
Hope that helps.