There's a filter in the washer that needs to be cleaned out periodically. Call your manufacturer (or look online) to find out where the filter is. My husband actually sells washing machines and we had the same problem and didn't know why. Then, he went to a training that just happened to show the process for cleaning the filter. Ours is located behind the front plate on the bottom. We actually had to remove the filter cover with a screwdriver, but most machines have an easier process. After cleaning all the lint and lost coins out, our washer worked perfectly again.
Could be the timer. Check the other cycles like perm press, ect, and if it spins on those, then its the timer for sure. I really need more info on what it does to be sure.
sounds like your spin cycle has gone out on the cycle switch the knob where you set the cycle at.you can replace it get the mod.# sn# make and call who ever makes that paticular washer,or you can even go on line to sears total parts web sight and order it