When the cycle doesn't advance, it's probably the timer or a cold-water supply problem:
It's the timer, if your washing machine fills with water and begins agitating, but the timer never advances--or if the washer is in a spin cycle and the timer won't advance. Then you need to replace the timer.
Check the lid down safety switch. On the lid there is a small spike that goes through a hole when the lid is down.
Under the hole is a switch that allows the timer to advance and the washer to spin only when the lid is down. Two screws hold the switch in place and the plastic switch will sometimes break and be hanging by the wires.