Maytag top loaded washer LAT 8608AAW. The belt going to large center pulley burnt and cracked so I replaced it. The other front belt is a little streached but seems OK. The washer does fill, spin, empty water etc OK.. But in the wash cycle it fills OK but the drum [agitator] never rotates back and forth so the clothes never get washed.

You mean the agitator does not rotate, right? If it was working prior to replacing belts, then you need to double check the belt - probably the longer one. The smaller if I recall - goes to the pump, and apparently it is doing fine.
You did use a factory belt or equivalent, I suppose? The bigger belt going to the center is designed to slip some so that when it goes into spin, it will gain speed gradually. If it is too big or loose - it may pick up on the spinning - but not on the agitation.
Educated guess from being in the sales end of it. Hope I am right.

That Noes is absolutely correct! :D I think he is Old Lonely in disguise! :eek:
If you bought that belt in a hardware store, it WILL NOT work! The "V" angle of the Maytag belt is not the same as an ordinary 1/2" belt. You need an original Maytag belt, part number 2011125, which is the DRIVE belt. But having said that, I always recommend relacing the belts as a set. The pump belt is a 2011124 and it has to be quite a bit looser than the drive belt when installed properly. DO NOT move the pump in order to adjust the smaller belt otherwise the drive belt will slip.
Before replacing the belts on that machine, you should check the center pulley and make sure it is not overly difficult to turn with the belts off. In one direction it turns the drums which has some resistance and the other direction it moves the agitator. If it turns with a lot of resistanceduring the agitation direction of the pulley, then you have a bad transmission. Depending the age of the washer it may or may not be worth installing a new trans. In our area it's about a $400 job because besides the trans you must also replace the center seal assembly and the outer tub bearing kit in most cases.

I thank both of you for the expert help. I did call a Maytag dealer got their # AH61808 V BELT,DRIVE PULLEY (Drive Belt - 41.5 inches long) the correct replacement belt. Had I read your answers before getting the belt I would have gotten both belts. After installing the belt everything worked except the agitator did not turn. Soooo I took the belts off and I had my wife watch as I turned the big pulley both ways and she said the drum did turn but she said nothing about the agitator. I 'did not' know what turned the agitator so I just got a mirror and went down and turned the pulley clockwise and the drum rotated OK. I turned the pulley counterclockwise and there was a small space and I hear clanking as I keep turning but the agitator did not rotate. [When we tried the washer with the new belt I did not hear any clanking noise.] There was a little resistance when turning the pulley but I would not say it was excessive. With your expert help I know the transmission is in fact gone.

The cost of a repair does not make sense because of a few reasons. The old age of the washer and the kids are now gone and we retired people don't have a lot of washing to do any more so a new smaller washer will be more cost effective. My wife and I thank you and Ask Me Help very much for all your expert help.

Wise decision! It is definitely a bad transmission from the way you describe the results of your test. In the "old days" we always used to repair transmissions but in most cases it's not worth it anymore.
Good luck!