Admiral washer willl not spin

Hello. I'm a little confused at the description of the problem. You indicated it, "will not agitate during wash cycle or spin during the spin cycle." But later in your description you indicated, "It will however, drain and spin after wash cycle and during the rinse cycle." I'm not sure if you description was an error but it sounds like you will need to replace the coupling which is part number 285753A.

Your washing machine top lord or front lord?
If your washing machine top load you have cleared drain valves in have blocked then check drain motor like that as you can check which model or type

Likely to be the clutch or gearbox wear.

What is the model number of the unit?

call manufacturer. heard there was a recall... for dangers of fire.

sounds like the washer transmission has failed.

If The washer won't agitate
Check to make sure no clothing got wrapped around the agitator. Check the lid switch, timer, and drive belt, other potential causes, such as a bad transmission or bad agitate/spin solenoid, but they are much more involved.
if the washer won't spin, the lid switch, timer, drive belt, transmission, or agitate/spin solenoid could be the cause here as well. Sometimes if the load is unbalanced or too heavy, the washer won't spin. Take some of the clothes out and try the spin cycle again with a lighter load.

Here are the steps to replace the agitator.
1: Take the fabric softener dispenser off and pry off the agitator lid.
2: Use a socket wrench with an extension bar to remove the stud and seal.
3: Remove the agitator top and bottom.
4: Check the agitator clutch assembly (located in the agitator top) for excessive wear.
5: To replace, just reverse the directions.

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