The actual DC connector jack in the pedal housing may be bad. When the barrel connector on the power supply plugs into that DC jack, it actually pushes on a small, springy metal tab. It acts kind of like a switch. When the power supply is plugged in, the 9 volt battery is switched out of the power circuit. When the power connector is not plugged in, that tab is supposed to make contact with a terminal inside the jack that is soldered to the 9 volt battery connector. If the terminal is corroded inside the jack, the metal tab may not be making a good enough contact and it will be as if the 9 volt battery is switched off.
Try spraying some De-Oxit or similar electronics contact cleaner in the DC power jack. A better option would be to replace the jack, especially since there is some history of corrosion with the pedal.
Good luck!