On the wash cycle the agitation is very slow.The spine cycle is fine

The cycle controller

have a look at this link might help.
washing machine agitates really slow Google Search

I hope you are referring to the agitator.
On washing machines, the drum only spins one way.
The agitator in the middle of the drum will spin both ways.
If your agitator only spins one way, something is broken.
Please share the year (?), make and model of the machine.
God bless your efforts.

Need model number! Do a google search for a manual (just search by model number). Repair parts and some troubleshooting help at: http://www.repairclinic.com/

sorry the repair is a new gearcase appx 230.00 plus labor in your area or buy a new washer ,,,,,

replace the clutch assembly for the fix.
Phil

Check the motor for proper oltage. The motor controls everything from spining to agitator.

change the drive coupling.

The tranny should either spin or agitate not both

Your transmission is not engaging thats why the speed changes your making will sometimes get it to work.Honestly any machine after the 10 year age mark is not worth the cost of replacing the transmission.