The NSS only allows the car to be started in PARK or NEUTRAL. The starter won't engage if the car is in any other gear. The NSS also turns on the reverse lights when the shifter is put into reverse.
There is no "wire" on the trans that would make the car not move. There is "kickdown linkage" that goes from the carb to the trans. That linkage increases the transmission's line pressure when you press on the gas pedal. If the car was driven without that linkage, the trans might be hurt internally. Check to make sure there is a NSS screwed into the trans on the drivers side. Then, make sure the trans is full of fluid.