My Sears Tractor had the same problem. Found out the shifting mechanism was rusted/corroded into the transaxle case. Where the shifter rod enters the case there is a rubber o-ring, square-sectioned,
seal (of sorts) that was broken, which I super-glued back together. I assume the broken seal/ring allowed water to enter the transaxle and it rusted the shaft. I also found the 5/16ths detent ball in the shifter to be rusted out of round--found a new one at Ace Hardware. Even after the transaxle was out and split, the shifter would not budge. Three days of soaking in Kroil and a three-lb. hammer--out it came. Works good now.
Steady Eddie
Steady Eddie, September 2004