If your GE washing machine isn't spinning, close the lid. Your washer won't start spinning with the lid open. If the lid is closed, check the lid switch, which lets the control board know that the lid is shut. Unplug the washing machine, and remove the main access panel. Test the switch for continuity using a multimeter. Replace it if it's defective. Verify that the washer hasn't paused between cycles. Close the dispenser drawer on front-loading models. See if you have blown a fuse or tripped a circuit breaker, especially if the washer was running and stopped.
If water isn't draining, check the drain hose, which is located on the back of the unit. Turn off the water, and remove the hose. See if it's dirty, and dig out clogs with a plastic utensil. Straighten the hose if bent, or replace it if it's badly kinked or crushed. Only allow up to 4 inches of the drain hose into the tub, and remove the extra. Do not install the drain hose more than 8 feet above the floor for a standard washer and only up to 5 feet above the floor in compact units. Clean your home drains, if clogged, using plumbing products or tools.
The pump actively moves water out of the tub during the spin cycle. If the pump isn't running, unplug the washing machine, and remove the main access panel. Remove any clothing or items caught in the pump. See if the pump has broken components, especially the impeller. You must replace the whole pump since it's difficult to repair individual sections of the pump. Check the pump pulley, and see if it's frozen. If it won't turn easily, get a new pulley from a GE parts dealer.
The selector switch is located on the control panel. Verify that the button is properly set. Test the switch with a multimeter, and see if it's working properly. If not, you need a new switch since it's hard to repair this part. Check the internal belts and clutch. If these components are worn or broken, you need new ones. While not common, the transmission can go out. Examine the transmission, and see if it has broken gears or is leaking oil. Unless you know how to rebuild the transmission, you need to replace this part.