Not necessarily. A typical test light requires 12v and only 0.5 amps and a solenoid will click with minimal amps as well. A starter obviously requires a lot more. Do you have a multimeter? Disconnect the main power wire to the starter and check the resistance of the wire from end to end, should be no more the 5 or so ohms. Check for corrosion or damage. Do not check resistance on a live circuit, it can damage your multimeter.
Also, try tapping on the starter with a hammer while someone turns the key.