Admiral Washer model #LNC6757 will not agitate

POSSIBLY A BAD CONTROL BOARD

It is either the inlet velve or the cycle programmer faulty

The water level switch may be going bad. As the water level rises to the proper level, it switches a set of contacts inside to stop the water fill and cause the machine to start agitation. Make sure machine is empty before you replace the water level switch---it works off of air pressure from a small hose attached to it.

What is the model number of the unit?

Normally yes. There are around 12 to 20 gallons of water in the tub after the wash cycle, which will be anywhere from 63 to 110 pounds of weight in addition to the weight of the clothes. For the machine to start the spin cycle to remove this water would place a heavy load on the motor, gearcase, pullys, belts, gears, ect. With the water drained, the load is lighter, and much easier to start spinning the excess water out of the clothes. The normal cycles are: Fill, Agitate, Drain, Spin, Rinse Fill, Agitate for rinse, Drain, Spin Cycle and off. Imagine trying to spin a 5 gallon bucket of water over your head, full of water, and then empty. Which one do you think would be easier to do? And safer for you.

sounds like the washer transmission has failed.

Most noises from a washing machine occur during the spin cycle. If you hear loud thumping during the spin, the load of clothes may have become unbalanced. Stop the washer and redistribute the clothes, then re-start it. Repeat these steps if necessary. 
for detailed help with diagrams and step by step instructions click the link http://www.applianceaid.com/washerspinnoise.html

yep you got it

ON THIS MACHINE WHEN IT AGGITATES MOTOR ROTATES ONE DIRECTION, WHEN IT PUMPS OUT AND SPINS IT ROTATES THE OPPOSITE DIRECTION. YOUR MACHINE IS ROTATING THE WRONG DIRECTION WHEN IT FILLS., INDICATING THAT THE TIMER IS SENDING VOLTAGE TO WRONG WIRES. SOLUTION , REPLACE TIMER.
PS: MAKE SURE ALL WIRES ARE PLUGGED IN TO MOTOR. WHILE THIS IS UNLIKELY , I HAVE SEEN THIS BE THE PROBLEM.

FXIT

FXIT

FXIT