Final answer:
The most likely cause of the brakes functioning without power assist when the engine is off, but normally with the engine running, is a vacuum hose blockage. Brake fluid leakage, faulty brake calipers, or worn brake pads would impact braking at all times, regardless of the engine state.
Step-by-step explanation:
When it comes to a vehicle's vacuum brake booster, it is designed to use the vacuum generated by the engine to assist in the braking process. With the engine off, there is no vacuum available to provide power-assisted stops, which explains why the vehicle would have no power-assist when the engine is not running. However, if the brakes work normally with the engine on, it suggests that the vacuum-assisted system is operational during engine operation.
The most likely cause for the lack of power-assisted stops when the engine is off, but normal operation when the engine is running, is a vacuum hose blockage. If there was brake fluid leakage or faulty brake calipers, the brakes would not operate normally even with the engine running. Similarly, worn brake pads would affect braking at all times, not just when the engine is off. Therefore, the issue lies in the vacuum supply, which is affected by the state of the engine.
In power brakes, as in some construction equipment like bulldozers, a motorized pump does the work in the system, maintaining vacuum consistently. Still, in most vehicles with a vacuum brake booster, the vacuum is only present when the engine runs. Also, it is important to note that air in the brake lines can affect brake efficiency as a gas is compressible; thus, air needs to be bled out for proper braking.