The Machine Part is in the Gym, next to the pool, by the inflatable tubes.
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Find the machine part in the cerulean city gym give that to the guy.
In the end of the tubes in the North.
The Machine Part for the power plant is located in the water at the Cerulean City gym in the very small square pool to be exact. Press A at the water to use Surf then check each spot of the water by pressing A you should eventually find it.
Go into Misty's gym and act like u were going to face Misty but instead go to the beach stuff on the left side of the gym face it and press A it Should say obtained machine part then take the machine part to the power plant.
in heartgold, if you are in cerulean city, you must go into the gym and go around every thing and the machine part will be in the inflatable tubes i think it will work in Soulsilver as well