The PARK system is completely mechanical. The easiest thing to check is the linkage. Disconnect either the cable mount from the rear of the transmission pan or cable end from the lever and verify the sector lever is actuated all the way to the PARK position (forward).
If the sector is fully actuated and the transmission does not lock the output shafts, remove the trans oil pan and check the park pawl linkage, springs, and shot pin (at the end of the linkage rod/spring).
If the shift lever on the steering column will not go to the PARK position with the cable disconnected at the transmission, the cable or steering column needs to be investigated.