Sounds to me like you have a 904 from a 64 or earlier with whats called the "ball and trunnion" front flange. This is not a basterdized ford product but an actual Mopar installed item. After 64 they went to the conventional style slip joint U-joint set-up. In 1965 only the 904 and 727 trans had the slip joint front, but retained the pushbutton capabilities. If you can find a 65 trans, you can either remove the tail shaft and replace the entire assembly on your trans so you retain the cable operation but have the U-joint tail, or just replace your entire trans with the 65. The whirring sound is not normal or good, and it sounds like a trip back inside is in order. I would have to hear it to identify the problem, but I would not drive it until it has been diagnosed. Take it back to the trans shop and have this checked immediatly. Good luck with the Dart. Geof
