Mintaka - “Square root graphs only go on forever theoretically.”

It isn't theoretical, not only can it be proved to go on forever, it can be proved it is continuous on the interval [0,∞).
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Mintaka - “it would appear there would be no room for an infinite graph of the sqrt (x)”

The graph of a function consumes no space.
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Mintaka - “Energy cannot simultaneously be non-existent and yet causing collisions of virtual particles in quantum vacuums”

The energy of virtual particles is not well defined, as they do not strictly require it, this is one of the reason they are called virtual.
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Mintaka - “There was NO energy, no time, no mass or matter, no virtual particles, no vacuums, no nothing!”

And what is the probability for a system in that state to evolve to the state we see today? Simple, if the conserved quantities are the same, it is non-zero. Which conserved quantity are you suggesting is different, thereby making the probability 0?
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Mintaka - “Universe-from-nothing theories require energy to get things started.

No they require mechanisms to produce huge but equal amounts of positive energy and negative energy (thereby keeping the sum fixed at 0).
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Mintaka - “Most theories of which I'm aware, however, simply presume that energy was just "there" in the beginning.”

Then you are several decades behind.
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Mintaka - “I believe the universe still requires lunch money.”

I have a friend who believes the Cleveland Indians will win the world series at the start of every season, despite all the evidence to the contrary.
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Mintaka - “But maybe it's more like a fifty-pound sack of potatoes on one side of a see-saw and a fifty-pound bag of apples on he other.”

That isn't how conserved quantities work. First off potatoes and apples both have positive mass.
What is the electric charge of a hydrogen atom? It is 0; it has one unit of what is defined as negative charge, and one unit of charge that has the opposite sign of the negative charge (called positive charge). The same goes for energy in the universe, there is energy we call positive energy---and there is another kind that has the opposite sign (negative energy). This is what allows there to be an abundance of energy (or charge for that matter) locally, while the system maintains a zero balance. Potatoes and apples don't have opposite signed conserved values.
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Mintaka - “Gravity is said to compress gasses into a natal solar core. But gas tends to resist compression and run-of-the-mill gravity doesn't seem capable of pressing inordinate amounts of hydrogen and helium into nice little nuclear clumps. What kind of energy is pressing gas into solar cores then?”

F=GmMr^-2? So when I said several decade behind earlier, apparently you are about 35 decades behind.
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Mintaka - “Are you suggesting that a probability is an actual cause of something in real time or in strictly hypothetical and theoretical terms?”

I told you that you either have to accept probability as a cause, or will find yourself with events that can not have causes; and I gave you an example of such an event. I don't have a personal preference for either outcome.
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Mintaka - “Our little galaxy is spinning at 168 miles-per-second, or about 600,000 miles-per-hour.”

I hope you don't teach kids that, since it is dimensionally inconsistent. You should give it to them in SI units, about 0.000000000000001 radians/second, but I guess that isn't quite as impressive sounding (hint: this is why you can't feel it!).

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I'm sorry this came off as a little rude, but your mis-characterizations of science and mathematics is getting rather tiresome.

Mintaka - "Let's also say all your zeros add up. This only describes the state of things now"

No, the universe is a closed system, so all those zeros have been static and always will be. That is how closed systems work, they never gain or lose any energy, the energy is but trapped into less and less usable forms over time. The thermodynamic laws themselves would not, could not work, if the universe were anything but a closed system. In a closed system, the sum total of energy at ANY point in time is the same as the total energy at ANY other point in time. It is, as Nyarlathotep said, time invariant in that respect. Now, if you want to imply or even deny that the universe is a closed system I would be happy to entertain the notion, but its scientific implications would be immense and would throw us squarely at a wall of unavoidable purely probabilistic causes much like the ones Nyarlathotep has already discussed, to the point that the variance of energy over time would have to continually be equal at any point simply by "accident".

Frankly, any such argument would strain credulity and be quite impossible simply based on the loose observations Newton made centuries ago.