Here are some possible causes and what to do:
* Park Pawl (most likely): The park pawl is a mechanical device inside the transmission that locks the output shaft when the shifter is in Park. Wear and tear, broken components, or low transmission fluid can prevent it from engaging properly. This is the most common cause of this problem.
* Transmission Linkage: The linkage connecting the shifter to the transmission could be worn, bent, or improperly adjusted. This prevents the shifter from accurately selecting Park.
* Transmission Problems: More serious internal transmission issues (low fluid, worn components, etc.) could also contribute. This is less likely if the problem only occurs when parked on a slope.
* Shift Interlock Cable: A broken or damaged shift interlock cable could also be contributing. This cable prevents shifting out of park unless the brake is depressed.
What you should do:
1. Do not drive the vehicle: This is crucial for safety. Rolling unexpectedly is extremely dangerous.
2. Check the Transmission Fluid: Check the transmission fluid level and condition. Low fluid or severely burnt fluid indicates a more serious problem.
3. Get it to a mechanic immediately: This is not something you should attempt to fix yourself unless you have extensive transmission repair experience. A qualified mechanic can diagnose the specific problem and perform the necessary repairs. They'll need to inspect the park pawl, linkage, and potentially perform a more thorough transmission inspection.
4. Mention the symptoms clearly: Explain to the mechanic that the vehicle rolls even when in Park, requiring the use of the emergency brake and a neutral start. This helps them focus their diagnosis.
Ignoring this problem could lead to accidents. Prioritize getting it professionally assessed and repaired as soon as possible.