From the description I would guess that the belt that runs the tape player is broken (yes it runs a teeny tiny belt from the motor to the spools) no belt means = no turning (i am assuming that the adapter requires the turning to work, i remember that most do but i have been wrong before, twice i believe lol)
Seriously, time for an upgrade or remove the player and take it in to a car audio store for repair (and take it out yourself do NOT have them remove it for you---way expensive for what they have to do)
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