My Maytag washer will fill on the Regular cycle, but only “click” when it is supposed to agitate. It continues to “click” to advance through the cycle and then will spin and empty. Same thing on the Permanent Press cycle. Funny thing is that it works normally on the Delicate cycle. Is it a timer issue or a 2 speed motor issue? Something completely different? I know I have an old Maytag–nearly 17 years old, but I have heard that I have the “last of the great Maytags.” I have six children and this washer has served me well all of these years. I have learned how to repair my dryer and would love to be able to fix my beloved washer 
It could be the motor but I think it is more likely the timer. Change it out and see if that fixes it. If you buy from this site and the part does not fix the problem you can return it, see the returns policy.
I’m having this same problem. I have a lat9605aae, and it will only work on delicate mode. It seems as if Regular quit working first, but I could put it in Perm-Press and it would work fine. Now Perm Press doesn’t agitate either, but it will agitate in Delicate mode. Not sure what to do? I know there’s an answer posted but that was 3 years ago. Please help. thanks in advance