Transmission slams real hard!

Hi I have a 2003 Saturn ion 3 with a automatic transmission. It won't move forward unless you kind of punch it! Then it slams really hard and I got it going in like 2nd gear, but rpms did not go up much at all driving it like that. I was 100 miles from home so I had no choice! It ran like that as long as you did not have to stop! If you had to stop, you had to punch it and have it slam again. Also, if I use my front brakes, the car jumps up and down! If I use just my back Breaks it stops ok. I do not have any problem with my Brakes! I looked at them real good to make sure! They are fine. The car will go into reverse and drive just like it's suppose to with no problems. I would like to know if the transmission input sensor & the output sensors could be the trouble? I heard a lot of cars get sent the junk yard because they thought the transmission was all bad, when it was just the input & output sensors. Does anyone know what the trouble can be if not the sensors? Thank you for your time.