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Remove the lower unit to isolate the problem. OR simply disconnect the shift rod coupling behind the access plates. Lower unit might be full of rust. OR shifter lever might be seized where it goes through the cowling. OR shifter shaft might be seized where it goes through the midsection housing.
Tried turning throttle to lowest idle ?
See post #3. Is there any jiggle at all at the shifter lever? If not, that likely is where it is seized. But if no jiggle at all, it probably is seized there the shaft goes through the housing. If the second is true, it is a pretty big job, requiring removing the whole assembly from the motor mounts/cowling shell. See parts breakdown on this website.
Do a complete evaluation of the motor before you spend any beer tokens for parts.