The drive coupling is the first choice but by far not the only, get in there with a multimeter and start eliminating possibilities:
If the washer won't spin or agitate, check the drive belt. If the belt is broken or if it isn't tight on the pulleys the washer won't spin or agitate properly.
Lid Switch Assembly
If the washer won't spin the lid switch assembly might be defective. This is a very common problem. The lid switch assembly can fail either mechanically or electrically. Test any electrical switches with an Ohm meter for continuity. The switches should have continuity according to their design.
If the washer won't spin or agitate the drive motor might be defective. This is not common. Check all of the other related parts to this symptom before replacing the motor. If the motor is visibly burned out or physically damaged, replace it.
If the washer won't spin or agitate the rotor assembly might be bad or damaged. The rotor is essentially one half of a motor, it interacts with the tub by creating a strong electro-magnet. If the stator fails or is damaged the washer might not spin or agitate. Check the stator for damaged windings or other defects.
Possible other causes:
Door Lock Motor & switch assembly
Motor Control Board