A resistor cart has coils of heavy wire that the cables connect to. They are inefficient as they use much more battery energy to run, as most of the energy is wasted as heat.
The controller cart has a small box that the cables connect to, and is much more efficient in that the motor is only supplied the amount of power it needs to run.
The batteries are the heart of an electric cart. If they are not in good condition the power and the range will suffer. Usually a decrease in range is a battery malfunction. There are other reasons too, but they usually reveal themselves to the operator. I would do the tests on the batteries and then go to other tests as needed. It is most important to start with the batteries and determine if they are serviceable or not! You really should have a DMM ( digital multimeter ) and a hydrometer ( for specific gravity of the electrolyte ) to do testing on an electrical cart. Both these items are inexpensive and obtainable at any hardware or automotive parts store. I'll post a link to " scottyb's " site ( he is one of our sponsors ) and read everything he has on his menu with the word " battery " in it! You will get a much better understanding of cart batteries and their functions.
http://www.cartsunlimited.net/