Ford Explorer makes clicking noise when trying to start and engine won't turn over but the battery still works?

just because you lights and radio work does not mean your battery is good.the starter needs over 100 amp of power to start a car a light needs 5 amps, load test your battery and check cables and connections for corrosion. if battery is over 3 to 4 years your due for a battery, also check alternater is charging when car is running