A a GE dishwasher doesn't agitate, first, check the cycle selection. Some models have a lengthy soak cycle, during which time the washer will not agitate.
Some GE washers have a small plastic piece mounted into the bottom of the open lid that is designed as a sensor to alert the washer once the lid is closed, at which time the washer will begin to operate. If the sensor piece is malfunctioning, the washer will not operate even with a closed lid. Investigate the sensor to ensure it is still operating properly.
After confirming that the sensor is functioning, attempt to reset the water level in either direction to make sure that the switch is working properly. Do the same with the speed selector switch to confirm that it isn't stuck.
If the washer is making noises, but is able to fill with water, it is possible there is an object stuck in the line. If that is the case, turn off the washer and contact a repair service.