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From what you described and tried, your problem may be in the powerpack wiring connector, the boat or motor harness, or the pack itself.

You didn't provide the engine model so we have to talk in generalities until you do.

The black/yellow "kill wire" gets grounded to turn off the ignition system. If there is an open circuit anywhere in the system, the motor will not shut off. Check the wiring connections for bent or broken pins that are not making contact. Look closely at the black/yellow wire connector at the powerpack and at the boat to motor connection. You should also make sure that the black ground wire at the key switch is continuous all the way back to the engine block.