If the heart becomes damaged or weakened, how will this affect the body's systems?

Think of blood as a gas / fuel for the car (your body). If there is no fuel, there's no movement (dead) so when the fuel tank is damaged the car won't function properly.

So if the heart becomes damaged, or weakened it would start making blood clots and damage the organs that need blood to function properly. The circulatory system wouldn't function properly and because other organs depend on the circulatory system it would cause a chain reaction, affecting other body systems.