The washer gets stuck in the agitate cycle.

no
some cycle the agitator during the fill cycle to get better distribution of the clothes as it is filling and then shut of the water and proceed to the wash cycle
have a technician check out the program board

Heck your warranty--sounds like the cellonoid is sticking

Remove the front panel and open the control panel. Check all wires for loose or broken connections.

Bad timer. Try to find a used one if possible, this item is a little expensive.

Hi,

It sounds like it could be the coupling that has worn or broke, to verify this put the washer in spin, let it drain the water out (if it will) then turn off the timer or open the lid, wait 10 seconds or so then start back up in spin. If the washer just whines then it is most likely the coupling. I have put together some instructions on this if you follow this link it will tell you more about it and how to replace it if you wish. Let me know if this helps.

http://www.fixya.com/support/r4670549-drive_coupling_replacment

sounds mor like the pressure switch is stuck closed

Please be carful as running the agitator without enough water will overheat and kick out the motor, however it should be ok when it resets itself.
Yes, the machine should stop agitating when you lift the lid so this too is part of the problem.
After looking at the print I can only suggest that the cam contacts in the timer ( contacts 12 and 14) that start the motor are burned and stuck together.
Quentin

On most Amana washers you pull on the agitator with brute force. It "snaps" on. It helps if you fill the washer with hot water and let it set for a few minutes... drain and then try pulling it out. When i last took apart my Amana it took me and a friend to pull the agitator off.

what kind of click are you hearing like a timer advancing or a hum them a click about every 10 minutes and dont rate me yet till were done

you must unplug the washer for just 1 minute open and close the lid 10 times and plug it back in and put it on a light load cycle and let it wash with empty load. shoul work fine after that