| Before you replace the solenoid, check the small white connector that pushes into the back of it. These are notoriuos for playing up and exhibit the symptoms you have.
You can close the terminals in it a little with a small screwdriver or such like. so they grip a little better on the pins in the solenoid. When you refit it, pass a small cable tie between the two wires and around the solenoid to hold it in place. | 
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