Battery replaced but my positive connector is dark.

A dark connector could be a sign of oxidation which can cause a voltage drop. Try scraping it with sand paper or a file. Battery corrosion can be cleaned with hot water, baking soda and a tooth brush. The Toyota starter has a heavy duty relay on top, it is a starter solenoid with a replaceable plunger and two contacts which frequently are the cause of a clicking sound accompanied by a no start condition. Ensure your battery is fully charged and is not the cause of a no start condition. Are your headlights bright? Try jump starting the car using another car and jumper cables and see if the car starts. Cycle the ignition key to the start position ten or fifteen times sometimes the starter solenoid will engage.