Well, now.
First of all, it's worth noting that when atoms are compressed down to where the electrons and protons get smashed together, if there is enough energy, you wind up with a ball of neutrons; the protons and electrons combine, IOW. The environment in which a black hole is theoretically created is the center of a supernova; and we know that slightly smaller supernovae create neutron stars, so this is relatively well understood, because we can see neutron stars and cannot account for our observations in any other reasonable way. So most likely, what exists initially inside the event horizon of a black hole is a ball of neutrons. What happens to anything that falls into it after that, we cannot ever know; once the event horizon has formed, the only way anything can get out is Hawking radiation, which means that all we see is a "gas" of escaping particles. We get no details from this about what's inside of the hole, other than mass, charge, and spin. This last is the relatively famous "no hair" theorem, "a black hole has no hair," a rather amusing statement meaning that the internal characteristics of a black hole are impossible to determine; its only characteristics are those of the whole hole (heh), rather than any constituent of it.
Now, your question is more interesting than that. But you need to understand what the differences are between the interior of a black hole and the Big Bang to understand the answers I'll give, and before I start, I need to be sure that you understand that while this is all theory, the vast bulk of it cannot have been any other way. The biggest difference between a black hole and the Big Bang is that we are outside any black hole we can observe, but we are inside the results of the Big Bang. Therefore we have physical evidence we can examine that can tell us about detailed characteristics of what happened back then, a situation we can never be in with respect to a black hole.
Another important point to understand is that the statements about the visible universe being, for example, the size of a pea, make people think that the WHOLE universe was the size of a pea; this is not the case. We can only see out so far, because looking outward is necessarily looking back in time, because the velocity of light is finite. Thus, in a universe of limited duration, there cannot have been any light before its beginning, and thus any point at a distance further than light could have traveled in the amount of time since the beginning is invisible- it is "beyond our horizon." What is being said is not that the universe was finite and the size of a pea; the universe has always been infinite. What is being said is that the visible universe was the size of a pea. This is an important distinction.
OK, now we have a better idea of what we're talking about. We're talking about an enormous density, all of the matter in the visible universe packed into an incredibly small space. There is an implication to this: there is a law of thermodynamics that says that temperature and pressure are related to one another, and vary directly. In other words, as the pressure increases, so does the temperature. In practical terms, you can observe this when you pump up a bicycle tire. The pump and the tire get hot. And there is another law that relates pressure and density similarly. So the density of the universe is so high that the temperature is enormous, far, far beyond the temperature even at the center of an exploding supernova. At these temperatures and pressures, the very characteristics of protons and neutrons become "smeared."
You are probably aware that protons and neutrons are made of smaller particles called quarks; specifically, of three members each, of two types: up and down. Two ups and a down are a proton; two downs and an up are a neutron. Now, this enormous pressure and temperature mean that there is plenty of kinetic energy in these quarks, so much that they can easily turn into one another with only a very small change in their kinetic energy relative to the total that they have. Not only that, but it turns out there are four more kinds of quarks, strange, charm, top, and bottom, that they can turn into; we don't see these much these days, because they all decay into up and down quarks pretty quickly, but back then, there was so much energy around that they could pretty much freely interconvert into one another. And to top it all off, quarks are held together in threes by the strong force, and the strong force has a characteristic called "asymptotic freedom:" this means that if the quarks have enough energy, they don't have to stay together all the time, but if they don't have enough, then they are confined into the "bags" we call protons and neutrons (and a bunch of other particles, too, all called "hadrons," but because the heavier quarks decay so quickly, none of these lasts very long, and you wind up with protons and neutrons). So the enormous pressure of the universe had the interesting property that instead of pushing things together so much they couldn't do anything, it actually pushed them together so much that they COULD do anything, just about.
Another interesting thing is that when things get hot enough and high enough pressure, the forces we know of get "smashed" into a single force. For example, above a certain temperature, you can't tell the difference between the weak force and the electromagnetic force. We can actually slam particles together hard enough these days that we can reach that realm. At another higher temperature, this "electroweak" force can't be told any more from the strong force, the one that holds the quarks together; and this is pretty well above the temperature where the quarks begin to experience asymptotic freedom. We haven't made any accelerators that can make particles "hot" enough to enter the "strongelectroweak" realm, but we are finishing up one at CERN called the Large Hadron Collider or LHC that should be able to show asymptotic freedom, and we already have some that we believe have just entered this realm, the Tevatron and a few others. The last threshold is the one where the "strongelectroweak" force gets smashed together with gravity. We know really very little about this, primarily because we have not managed to synthesize an effective quantum theory of gravity; until we do, we cannot even imagine really what this would be like.
So take all this interchangeability, of both particles and forces, and this enormous pressure and temperature, and that's what things were like right at the Big Bang.
There is another realm beyond this: it doesn't just keep going down and down, cosmologists believe. What they believe is that there was another state of the universe before the Big Bang, called the "inflationary universe," which is when the dimensions went from being small to being big. But this isn't even really a theory yet; there's too little evidence left over because the Big Bang erased a lot of it. But it's a pretty strong hypothesis, there is some evidence left over, and it explains that evidence pretty well; it's just that it hasn't predicted anything yet, and there are also some interesting competing hypotheses out there. But if we get into that, we're going to be off into a tangent about string theory, and ekpyrotics, and a bunch of other stuff that's pretty speculative still at this time. Basically, the interchangeability, and the pressure and temperature, are what you need to keep in mind.
