If you can hear the motor running during the spin cycle I would take a look at the drive block it maybe stripped out.
I would remove the agitator, put the washer in spin and with the lid open watch the drive block. If you can something spinning around inside the drive block, but the block does not spin then the block is stripped out and needs to be replaced. Of coarse you will need to push the lid switch in with something to watch it with the lid open.
The drive block is under the agitator and is # 17 in this diagram.Diagram for WHIRLPOOL LSR8233JQ0 AUTOMATIC WASHER, COMPACT A/W
This video will show you how to replace it.http://www.youtube.com/watch?v=lsgl6PSQwtc
This is the drive block for your model washer if you need to order one.
WHIRLPOOL Washer Drive Block, part number: AP2905773
Check it out and let us know what you find.
It could also be the clutch slipping, but going by what you have told us I would look at the drive block first.