Thank you for your question and I understand your concern.
Your symptom seems to indicate two failures. The water level is controlled by the water level pressure switch. The water level pressure switch senses water level by a small amount of air pressure transmitted to the pressure switch by a pressure hose. The pressure hose is connected between the air dome and pressure switch. If the pressure switch is faulty or if the pressure switch hose has hole, the air pressure will leak out and the pressure switch will allow the washer to continue to fill. The pressure hose will need to be check for any holes. If the hose does not have any holes or leaks then I would have to suspect a faulty water level pressure switch.
As far as the washer not spinning; I do not have enough details in order to know if the motor is running or not when it should be spinning. If the motor is not running; it could be because of a faulty lid switch, timer or a motor issue.
I highly recommend calling a service technician to diagnose and repair your GE washer. You can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services