Ok...that sounds like what happens when the vehicle speed sensor's voltage signal is cut off or not making it to the PCM...This happens if either the VSS is bad, unplugged or the cabling leading from the VSS to the PCM is somehow damaged.
Check the VSS with a multimeter by putting either the rear or entire vehicle on jack stands. Then unplug the connector to the VSS but leave the sensor itself in place. Turn your multimeter knob to 'Volts' and then put the two leads onto the two terminals on the sensor. Spin the driveshaft to see if there is any voltage being generated as you spin the shaft...If nothing is happening, the sensor is bad...If the sensor is producing voltage then that would indicate it's functioning. Alternatively, if you have another vehicle w/the same sensor that also works normally, you can try swapping it to see if anything changes...