The "charge pump" in the transaxle supplies oil for the hydraulics and keeps the hydrostatic pump and motor circuit charged with oil.
Is the drive belt from the engine turning the pulley and cooling fan on top of the transaxle? If the pulley and fan are turning, there may be a key or splines sheared between the pulley and the transaxle input shaft.
Inside the transaxle, there is a pin that keys the inner rotor of the gerotor oil pump to the input shaft. These have been known to shear, too.