What is wrong with my car?

I was driving on the interstate the other day and when I tried to accelerate it didnt go anywhere but just made a loud whirring sound. I took my foot off the gas and tried again and it did not go again. I put my hazards on and rolled down to about 15 mph. When I accelerated again it picked up and went on home with no problems. Later on when I went somewhere it did the same thing, not going into any gears this time. It was rolling fine until I came to a stop and tried to accelerate again. It didnt move. I tried changing gears and it didnt go any to any of them. When I turned the car off and on again it picked up fine for a while then started the whirring. When I stopped and tried to go it would not go. I turned it off again and it went but at15 mph it stops again and wont shift until I turn it off and on again. The fluid is full and there is no serious debris in the pan. I regularly change the filter and fluid. I have a hunch it is the converter, but would like other ideas. 2000 Chevy Impala 6 cyl.