Ok, 72 volts is a pretty respectable power source. We could test it with a multimeter, but since you don't have one, we can do a different test. I don't want you to hook that much voltage directly to the motor though. It's enough to throw a heck of a spark and possibly injure you. 72 Volts WILL be enough to travel through your body.
This is what I recommend.
Disconnect the existing power wires from the motor so that there is no chance of that 72 volts messing us up.
Raise the drive wheels so that the Cart doesn't leave the area if the motor checks out good.
Now, with a set of jumper cables, attach to just one of the batteries in the cart if you know the batteries are all good and charged up. If you are unsure of the batteries in the cart, then use a known good car battery.
so, basically, I'm going to have you direct connect 12 volts to the motor to test it safely. That should be adequate power to make it turn fairly slow without hurting you.
If 12 volts doesn't make the motor turn, you may wire 2 batteries in series and repeat the test with 24 volts.
If the motor doesn't turn with 24 volts, it probably isn't any good. However, I don't recommend any more tests above 24 volts without a multimeter.