The problem sounds most likely to be a faulty gear selector switch. We would begin the diagnosis by checking all of the wires and connectors to make sure they are okay. Next, we would test the gear selection switch for proper continuities and also test the throttle to make sure that it is working.
If you are able to attach a photo of the throttle then we can see if we have it or if we are able to get it. The photo would need to show the throttle and the connector at the end of the throttle's cable.