The way you can test for a bad ground (which would be bad if it developed an open or resistive connecton; not from a short) would be to connect a 12 volt light bulb or test light, or a voltmeter between the engine block and the battery negative "-" post. If you use a voltmeter; the negative meter lead should go to the negative battery post, and the positive meter lead should go to the engine block. It is important to make contact with the battery post; not with the cable clamp that attaches to that post. So you may have to touch the meter or bulb lead to the top of the battery post, through the opening in the center of the battery cable clamp. Run the starter while the test device is connected to both of those points, and measure the voltage on the meter, or see if the bulb glows. If the meter reads more than 0.7 volts during this test; or if the bulb glows or lights up, this means that the ground connection or the battery cable clamp connection is bad. If the bulb does not light, or the meter reads less than 0.7 volts; then the ground connection is good.
But from what you last wrote; it now seems very likely to me that the starter solenoid is bad (not conducting the amount of current the starter needs), and that is what is keeping the starter from turning the motor over. When you say the motor does not turn over; there is no way to tell whether the motor does not turn because it is tight or binding; or whether the motor does not turn because the starter is not putting enough force on it. I understand that the starter has already been tested and found to be good; but I believe that when Auto Zone tested the starter, they did not separately test the starter solenoid. If the starter solenoid is bad; it will make the starter cut off after a few seconds, even when there is nothing wrong with the starter. And that is exactly what the car is doing. So I recommend replacing the starter solenoid.