If it helps you get your head around things, the whole thing works by varying the tension in the front belt which works against the tension in the rear belt.
The rear belt tension is trying to push the sliding pulley down and is balanced by the tension in the top belt trying to push the sliding pulley up.
The rear tension is fixed by the spring under the seat and the front belt by the bigger spring under the axel.
Moving the speed selector alters the balabce between the two so the slider moves changine the drive ratios.
Something is stopping this happening.
If the back turns freely without the front pulley on and the front belt drives happily without the rear on then the sliding sheave itself is the likely suspect.
You can download the MTD manual from here
mymowerparts.com/pdf/MTD-Service-Repair-Manuals/
You are looking for the "Must Have Book 2"