Zombies would initially be fast (provided they are the standard Romero type). Until they under went rigor mortis some time after death.
Sadly however Romero zombies can't exist thanks to certain chemical exchanges within human organisms which are required for locomotion and are obtained via breathing. So zombies now have to breath.
This isn't too problematic as the majority of zombies are now popularized as infected individuals under the influence of some pathogen. Theoretically said virus could colonize in the brain and disrupt or destroy certain vital brain functions such as the limbic and neocortex.
What makes it harder to justify the zombie is post mortal functionality. In theory the vector could contain some sort of recombinant dna sequence that allowed it to highjack the body, though this would mean it would be more likely that the vector is a weaponized virus, which isn't outside the scope of probability, but unlikely with today's standards of biotechnology.
So the virus could take up position in the brain/stem, and using specialized rdna for the purpose of sending electrical impulses, gain control of a human body after destroying the reason center and or stimulating various other impulse centers compelling the infected person to feast on the flesh of others to simultaneously gain sustenance and spread further infection, until they ran out of people to eat and starved to death.
This could potentially work to keep the host alive. I'm not keen on all the nutritional values of human meat, but if it contains enough of the right nutrients then it could keep the infected going until other virus/bacteria entered the host and begin to damage the host cells. So the more successful a single infected person is, the faster they will self-destruct under a barrage of secondary infections/running out of food in a given area.
In short. Zombies can no longer be "undead".
Edit:
http://www.undeadreport.com/wp-content/uploads/2009/08/mr-t-knows-zombies.jpg
http://en.wikipedia.org/wiki/Adenosine_triphosphate#Functions_in_cells