Shift interlock solenoid?

You could but it would take some modifications. I would just fix it; can I ask if the brake lights work? If not, this will be the problem if so, the shift lock needs to be replaced or adjusted. Here are the instructions for that.

Place the ignition key into the "Lock" position. If the key cannot be rotated to the lock position, lift the adjuster button on the park lock cable and slide the adjuster rearward in vehicle (compressing the spring) and rotate the key into the locked position.
1. Place the park lock cable adjuster button into the up (unlocked) position.
2. Grasp the cable at the front of the spring and move it forward in vehicle to remove the slack and release the cable.
3. Move the cable adjuster rearward in vehicle 1.5 mm (1/16 inches) from the previous position. While holding this position, push the adjuster button down flush with the adjuster body.
4. If the shift lever will move out of the park position with the key in the "Lock" position or the key lock cylinder will not turn to the "Lock" position with the shift lever in the "Park" position the readjust the park lock cable or refer to Automatic Transmission Shift Lock Control System Check in Steering.

Check out the images (below). Please let us know what happens.