All four possible reactions in the animation are energetically favorable; the energy of the four products is lower than the energy of the original starting molecule. Why does the starting molecule not completely and quickly convert to its possible products before the addition of heat or an enzyme?

Starting molecules not completely and quickly convert to its possible product because an activation energy barrier exist that must be overcome for conversion to product.

Explanation:

The activation energy of a chemical reaction is closely related to its rate. This is because molecules can only complete the reaction once they have reached the top of the activation energy barrier. The higher the barrier is, the fewer molecules that will have enough energy to make it over at any given moment.

Many reactions have such high activation energies that they basically don't proceed at all without an input of energy. For instance, the combustion of a fuel like propane releases energy, but the rate of reaction is effectively zero at room temperature. Once a spark has provided enough energy to get some molecules over the activation energy barrier, those molecules complete the reaction, releasing energy. The released energy helps other fuel molecules get over the energy barrier as well, leading to a chain reaction.