You might have two problems; a faulty governor inside the trans preventing upshifts and misadjusted park cable. The shift cable and the park cable are separate adjustments.

The park cable is actuated by a mechanism at the base of the steering column inside the engine compartment; basically, when the shift lever is moved from Reverse to Park a separate mechanism takes over and actuates the park cable.

To isolate the "no upshift" problem, disconnect the rod that attaches to the transmission lever at the lever and allow the trans lever to come full forward. If it still won't automatically upshift in Drive the problem is internal.