It works fine on flat ground.

Because the whole weight of the car is resting on the transmission parking mechanism (which could break it) and you're trying to move the entire car, albeit a fraction of an inch, with the tiny gearshift handle.

Next time, set the "emergency" brake while in Drive, Neutral or Reverse with your foot on the brake. Then let off the foot brake to be sure the "emergency brake" is holding the car on its own. THEN put the transmission in Park, and you shouldn't have any problem.

To fix it now:
1. Get some strong helpers. Steeper incline = need more helpers.
2. Have them muscle the car uphill while you move the gearshift lever out of Park.
3. You may have to lightly touch the brake while doing this to get the internal lock to release. Don't push the brake so hard that they won't be able to move the car.
4. Be ready with the foot brake so that when the car is out of Park it doesn't roll back down on your helpers.

When the engine was off it slid backwards and put the transmission in a bind, have some push the car forward just a little and the pressure will ease and allow the trans to shift.
It happened to me too.

Check your tranny fluid if it is low it will be harder to shift gears, also check your engine and tranny mounts (the bad engine mounts on my Ford Taurus made it almost impossible to change from park while on an incline). Hope this helps.