Inclined to agree with gear box.. On the cables outside give 'em a slight "Tug" they should be tight, very tight in fact.
Now remove the trim above the slide out (usually, can be below but usually above) remove some plugs and the screws behind them
Youy should SEE the slide "Works"
ON the end of the motor NOT hooked to the gear box there is a 1/4" Hex shaft.. Size and shape sound like a common power screwdriver size? It should, it is.
Using a flex shaft you SHOULD find in your Manuals bag.. And a power drill. give it a try. No guarantees if the gear box is toast.. but well more power to you .