A key element to zombies is that they're relentless aggressive. Why don't they duck when you hit them? Why don't they show any sense of self-preservation? A couple of interesting theories in humans may point to the reason.
Researchers in Italy were able to find an actual switch in the brain that controlled fear response. When the switch was turned on, people reacted appropriately to fear or harm, so they would shy away when they felt threatened or they would hide from things they were afraid of. When that switch is turned off in that same person, the only way they can respond to fear is through aggression. If we think about this in terms of zombies, what that would mean is that a zombie that feels threatened by you can do nothing but act more aggressive. Attacking a zombie, beating a zombie over the head with a baseball bat, will actually make them behave more aggressively toward you than have them shy away from you.
Secondly, there's a rare disorder in humans called CEPA which creates chronic insensitivity to pain. Sufferers of this condition have the sense of touch just like everyone else. They can pick things up in their hand and feel it, but their pain response is completely turned off. What they'll do is things like put their hand on a hot stove and let their skin completely burn, or little children will break their legs while out playing and just continue to run around on the leg. If something similar to CEPA is occurring in zombies, this would explain why they're not responding to threats or fear, why they're not responding to pain.
One thing is certain, that zombies do have the sense of touch; they can feel. If you can't feel the ground under your feet, you can't even walk. They do feel; they just may not feel pain.