Most carts of your year are an AC system if your cart is an RXV the way you're describing your issue assuming the batteries are almost new sounds like a controller problem.
That being said to be sure you will need to have it tested by EZGO with their controller programer and test equipment to be correct. That system in 2009 -10 is made in Europe and since 2011 they have converted to a Curtis system that most shops have test equipment for.
As long as you have checked your connections for tightness you will be limited to test further without proper equipment.
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