Kitchen Large Electric Appliances - Kenmore Washer not spinning

I know that there are many threads dealing with this subject and I have read alot of them but I am still not sure what the problem is. The washer agitates, fills,drains fine but doesn't spin. It will spin slowly if it is empty and I give it a few hand spins to get it going. It isn't the lid switch, it isn't the coupler, the motor isnt making any wierd noises. I suspect that it is the clutch. It is either out of adjustment or is getting fouled by oil from the transmission. I pulled the cabinet off to have a look at things and there is an oily film along the bottom 4" to 6" the cabinet. If it is the trans then we will probably be getting a new washer. By the way it is a Kenmore Series 80 model #110 34832200

It is the transmission. The upper seal has started leaking and oil is getting on the clutch and it is slinging it around. The trans would need to be replaced unless you are good at replacing seals.