One dead battery will not stop a cart unless it is open internally (rare). You could put it in backwards and the cart will still run.
(may not have a back up buzzer)
The proper thing to do is have the batteries charged then do a time / voltage discharge test.
At the end of the test the batteries will be discharged. Take a v meter and find the battery with the lowest voltage. (do it quickly)
A battery load/ minute tester will cost about 350.00
If you try to use an automotive battery load tester you will grill a turkey before the battery will show any drain.
You could take it to a local golf cart shop. They should have the proper tester ( if not, do not let them touch your cart)
One thing to note here, They should be able to tell you how many minutes it took to discharge
your batteries and most important witch batteries were the weakest.
You don`t always need to replace all of the batteries. You can just replace the worst ones as you can afford them.
They will try to sell you a complete set of new batteries weather you need one or six. Mostly because the guy doing the test has no idea how to use the tester or his meter.
Stay with the 6, 8 volt batteries. These will outperform the 4, 12 volt batteries.
They are cheaper for a reason!