A bad 4th shaft/spline is a common problem because the shaft was not hardened. Replacement shafts are. I don't recall the cutoff year. The hub/shaft is part of the 4th clutch. No clutch no shifting/gear.
Good idea to rule out other possible causes but I would take the advice of Troy1 since he is a tranny pro and works on these POS trannies for a living.
Even if it were a solenoid it is still a major repair job which could cost in a range of $500 and up. See thread below which is in our Tips and Maintenance section for solenoids.
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