I have worked on some washing machines and found this site which shows a GE/Hotpoint
When you mouse over the parts starting at the agitator, and work down to the transmission, the drive and to the motor.
Appliance Parts from RepairClinic.com - Detailed Appliance Illustration
I believe the problem is the bolt that holds agitator in place.
Try to pull agitator up and see how far it comes up... it may
Lift out of the machine, you have the problem in hand... when
You push down the agitator engages...
If this is the problem you need to use an impact to tighten the
Bolt that holds the agitator in place...
Please rate my asnwer