Don't change the starter unless you first check that the solenoid is being powered when attempting to start. You'll need to get a wire with alligator clips attached to the solenoid terminal, alongside the car's solenoid wire, and run that to a grounded 12V test lamp. If the bulb lights when the key is turned to "Start", then time to pull the starter to exchange or repair. If no light, the problem is elsewhere, perhaps the ignition switch. Also, while that wire is attached to the solenoid, if the other end is touched to the battery + terminal, the starter motor should run.
Edit: I missed where you said "electrical getting to the solenoid", but that should be explained. For example, if you hooked a DVM between the solenoid terminal and ground, you might easily read battery voltage when the key is turned, appearing to mean the circuit is OK. But there could be a dirty or burned contact in the circuit causing thousands of Ohms resistance, and while there would not be enough current for the solenoid to work, the meter (because of its extremely high resistance) would show battery voltage or very close to that. This is why the recommendation to use a light bulb (and not a Voltmeter) to check the circuit.
Edit: I missed where you said "electrical getting to the solenoid", but that should be explained. For example, if you hooked a DVM between the solenoid terminal and ground, you might easily read battery voltage when the key is turned, appearing to mean the circuit is OK. But there could be a dirty or burned contact in the circuit causing thousands of Ohms resistance, and while there would not be enough current for the solenoid to work, the meter (because of its extremely high resistance) would show battery voltage or very close to that. This is why the recommendation to use a light bulb (and not a Voltmeter) to check the circuit.
