The timer dial has to be pushed in manually to get it to engage the gears (really hard to do). Now when we pull it out, the water does not come on.

The timer knob and or the timer may need replacing here is a link for checking and replacing
The inner knob teeth tend to wear off on the ge top loaders, so check that first. You might have also broke the screw tabs that hold the timer in place from having to push it hard.