Your gas pedal is connected to a micro switch that activates the first solenoid. If you are hearing that solenoid click when you turn the key on, then that micro is faulty or stuck.
With cart rear wheels off the ground, There should be five clicks as you press the gas pedal slowly. The first click is the main solenoid. There should be no movement of the wheels with this first click. On the next four clicks, the wheels should move faster and faster with each click.
Each of fhe solenoids is activated by the micro switches in that silver box with the plastic cap on the end. If you are not getting all five clicks, then you have a faulty micro in that box.
This info is assuming that you did replace all five solenoids and that the wiring is correct.