Remember the old saying that the human body is mostly water—about 60% by weight? Well, here's a little thought experiment. The atoms that make up our bodies are packed reasonably tightly together. But inside each atom is a lot of space. The electrons and nucleus take up almost none of the atom's volume. If the nucleus were the size of the tip of a ballpoint pen and sat at the 50 yard line of a football stadium, the electrons would be orbiting in the upper bleachers.
Or, if the nucleus were the size of the stadium, the electron orbits would be as big as the entire US. The tiny electrons would be the size of baseballs. To be a bit more numerical, for a Helium atom only 1 part in 1,000,000,000,000,000 is actually something other than empty space.
The point being: the vast, vast, vast majority of the building blocks of our body—atoms—are made of nothing. If you could squeeze all the empty space out of a human being you'd be left with something that weighed exactly the same but was a quadrillion times smaller. This would be an object with a diameter of about 5 microns. Still visible with a powerful optical microscope, but very, very tiny.
Something to think about.
This post is dedicated to ICP. (NSFW, and probably NSF just about everything else except WTFLOLBBQ.)
(Interestingly, the super-dense version of you described above would have to be about a million billion times more dense in order to form a singularity. This gives you an idea of how much more empty space gets squeezed out when the electrons and nucleus degenerate to their most compact forms under the force of gravity.)