i,m positive, you need to load test them not just check voltage......how old are they? its possible that you may just have a few that are failing under load but from your 1st post when you just press pedal down and it shakes and sputters......that along with failing reverse is lack of battery power........reverse only uses half speed thats why it quits all togather.....just went thur this exact thing with a 93 cart......but trust me you have a battery problem........and yes if you slowly press pedal it will go BUT how far?? load test the batteries you,ll find your problem......................
