If it filled with water then stopped, then its not the lid switch. Even with a bad lid switch it should still agitate. Are you sure that it did not agitate. Bad lid switches are very typical, its a very common failure. Spin the timer around to the start again and see if it agitates. If it sill does nothing, you have much deeper problems. Both timers and motors are costly, if its just a bad lid switch, I would say do it yourself, but if its something other than that, you may want to consider having a service tech come and trouble shoot it so your not just buying and swapping parts. If it absolutely will not agitate, then it could be a timer(except you already replaced that), could be the motor, or could be in the wiring harness.