It is a EZGO Marathon. "89-'92, but possibly '87 or '88 or even '93. It is a resistor cart so it is not solid state and no speed controller.
The wiring diagram is here:
http://www.buggiesgonewild.com/elect...rt-wiring.html Post #2 is the one I would use. I might have a better one. I'll see if I can find it.
I'm not a cart mechanic but I did own one of these for awhile. The first thing I would do is replace the battery in your volt meter. Those things give weird readings when the battery is weak.
The next thing is I would replace the wiper on the speed board. A common problem area and replacement part is cheap.
I think you have more than one problem. You need to determine the health of the battery pack. Difficult to troubleshoot a cart when the batteries are weak/shot.
Here's a picture of the speed board and foot switch wiper.