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It takes very little amperage as you are using the voltage to create magnetic flux lines. The wire in the solenoid is continuous so you are not doing any work. The only resistance is the natural resistance of copper wire (which is very low). The amperage to turn over the starter motor is a different matter. You can weld with the 225 Amps to 270 Amps the motor draws to crank the car.
Is the solenoid clicking? If so the start circuitry from the key is working. If you are not getting any juice out of the battery (a locked starter motor will draw infinite current, literally melting the starter motor cables) I would suspect the points inside the solenoid are burnt out, preventing the starter motor from turning over, or you have burnt brushes, or a burnt open winding in the starter motor. Any of the above; and it is time to rebuild or replace the starter motor.