Maybe the parasite didn't evolve in people.
As another post mentions, it would take a very, very long time for a parasite to evolve in such dastardly ways, and through all of human evolution, you'd think someone would have noticed this phenomena. Even assuming the zombie/vampire numbers are rather small, enough humans would see and survive zombie/vampire encounters and would begin to hunt down and exterminate the parasite responsible. Yes, some of the infected might survive the initial sweep, but people would start working on antibodies and vaccinations.
Clearly, this hasn't happened, so the zombie/vampires must not be so systemically linked to humanity. There are several types of mind-hacking parasites out there already. Some attack mice and rats, others fish, others ants. With all the interactions between humans and animals, especially all the kinds of animal that we kill, it seems quite plausible that somewhere along the way some people might be exposed to a new kind of parasite, one we don't know about because it doesn't usually infect humans.
This parasite, having evolved to take over the brains and bodies of a different animal, is clumsy in its human host, hence the poor motor control and loss of ability to speak. The parasite, which would normally induce its host to seek out its predator, guides the zombie to a safe location while it adapts to its new and vastly different environment; the human brain.
The parasite begins to re-form its host as soon as it enters the blood-stream, seizing control of muscles and nerves as it makes its way to the brain. Within a few moments of a bite, the human is merely a host. Within a few hours, the parasite is beginning renovations on a large scale. The parasite is in unfamiliar territory, so it seeks to make the human more like its intended host. The first step is to discard all the various proteins and chemicals that the parasite is unfamiliar with. These are expelled, sometimes violently, as cysts and abscesses on the skin of the host. When these burst, the contents mingle and form a sort of cocoon.
The next step is for the parasite to get the body in working order. This could be likened to the owner of a new house rearranging the furniture; the outside of the house looks the same, but the inside has been changed to suit the new occupant. This explains the brain being moved into the chest, as well as the newfound strength and speed of the emerging vampire. Because this process occurs in a dark space, the parasite installs a tapetum lucidium (that layer that makes cats' eyes glow), allowing it to see in the dark.
The vampire, now fully formed, emerges into the world with most of its functional memories in tact. Having spend a few days reforming its insides, as well as expelling large quantities of fluid and material, the vampire is hungry and seeks a meal. Its first choice is a zombie because not only does a zombie contain exactly what the newly ex-zombie needs, but it is slow and easy to catch. Additionally, the parasite has reordered the human digestive system, drastically weakening it. Any normal food, even raw hamburger, is too tough for the parasite's new digestive system to handle in anything like an acceptable time, so the vampire seeks out predigested food. In the zombie stage, the parasite is reordering things on a cellular level, so zombie flesh is already broken down, requiring very little effort to digest.
Failing to find a zombie, the vampire turns to the humans around it. The parasite can now be found in any part of the host body, including its saliva, so any human that is attacked and then abandoned will be infected. The fact that the parasite begins to take control of the host's nerves as soon as it enters the body accounts for the mythological "venom" that may numb or paralyze the victim while the vampire feeds. The parasite requires massive amounts of iron to survive and function which is why the vampire has an intense craving for blood. Most of the nutrients in blood are negligible in terms of energy intake, but blood contains iron in concentrated form, making it essential for the vampire. Because both zombies and vampires closely resemble humans, the parasite is attracted to humans over animals, perhaps confusing the human for a zombie.
Failing to find humans, the vampire will slake its thirst for blood with animal victims as their blood is little different from ours. If there are no animals nearby (which seems unlikely seeing as the parasite had to get into the human from something), the vampire will resort to feeding on plants. There is no nutritional value in the plants, but the vampire is famished and desperate. If there were no plants, it would eat rocks, however, just as a human becomes hungry long before he is in danger of starving, the vampire can survive for several days without food, even after it metamorphoses, because the parasite has stripped the host body of most of its energy-consuming processes. Blood-flow is diminished except during strenuous activity, and the parasite has cut most metabolic function, resulting in the 'cold-blooded' resting state. If needed, the parasite can kick-start the metabolism, allowing the vampire to survive in cold weather. In addition, the vampire need never sleep, seeing as sleep is mostly a chance for the mind to process what happened in the day and the host's mind is not really processing anything anymore. The body's need for rest is met by phases of low activity.
In summation: The zombie/vampire parasite displays the expected self-preservation drive but not the species-preservation drive because, since the parasite didn't evolve to live in humans, the parasite does not accurately identify the hosts its own species. The vampire consumes zombie flesh because its weakened digestive system cannot handle flesh that is not pre-broken-down, as is the flesh of a metamorphosing host. Humans remain unaware of this parasite because very few humans are infected and survive.
