My washer doesn't start spinning on it's own but if I reach into the washer and give the tub a push, it will start to spin on it's own until it gets up to full speed and then it spins normally. This is the case both on the rinse and the final spin. I replaced the lid switch but nothing changed. Well, that's not exactly true. With the new lid switch, the machine will spin with the lid open. But the new lid switch did not fix the problem of the machine not being able to start spinningon it's own.

The clutch is bad. You will need to replace this.