After removing, cleaning, and reinstalling the cluster, the speedometer is dead until 35 MPH, then BOING! it starts working.

What exactly did I do? Can it be fixed? And if the cable needs replacing, how do I make sure I don't ruin the new one?

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1982 300CD Petrol/Black Leather

Are you sure the cable collar is fastened tight? More than once I've had to go back and retighten the speedo cable collar after messing around with the instrument cluster.