Are quantum mechanics and determinism actually irreconcilable? As a preface, I am not a physicist.  I'm simply interested in abstract physics and fundamental principles of the universe and such.  As such, if you can provide an answer for the layman (as non-academic and unjargonized as possible), it would be very, very appreciated so that I can actually understand it.
Everything I ever learned about physics seemed to be built off of an assumption that the universe and everything in it behaved deterministically.  So it should always be a (theoretical) possibility that, given perfect knowledge of every particle and force in the universe at a given moment, we can calculate with 100% accuracy what the state of the universe will be in the next moment.
This of course assumes omniscience and unlimited computational capacity, which is why I said this is only a theoretical possibility.  However, we can define our closed system to be much smaller -- say, a bottle full of nitrogen and helium -- and apply this principle more directly.  And it seems like this assumption is absolutely necessary for scientific experiments to even take place or have any validity, since without this kind of determinism, the observations and the results inferred from them can't ever actually be trusted.
I don't understand quantum mechanics very well, but it seems like this theory breaks this assumption completely.  From what I understand, there is no way to predict what the state of the particle will be at the next moment.  The most I can know is that, given that a particle is in state A, it will next be in state B or state C.  There is absolutely no way to know for sure, and the only way to find out is to observe it actually change.  Furthermore, observations of this kind don't yield any insight into what other particles in state A will do.
So, in classical physics, laws used to look like this:
A -> B   [A implies B]

But with quantum physics, all of this is gone, and our laws can at best look something like this:
A -> ((B v C) v D) v E   [A implies B, or C, or D, or E, or ...]  

How does this not break everything physics is built upon?  The implications of this are seriously troubling to me, and I feel like it destroys everything I thought I knew.  Can anyone explain how this works in slightly lower-level terms, or show how it's still possible for the theories and laws of classical physics to hold any weight?
 A: NEWTONIAN MECHANICS:
Newtonian mechanics, as expressed through Newton’s laws of motion, gave us huge confidence about our understanding of nature. We were able to calculate the motion of planets and predict their position quite accurately many years into the future, and then observed them to check they do as we have predicted. Things worked extremely well. Occasionally there were some disagreement between our predictions and observation, like the anomalies in the motion of Uranus for example. But these did not mean the Newtonian laws were wrong; we simply missed something out, and in the case of Uranus it was a planet beyond it that caused the anomalies. The physical properties of that planet were all calculated and predicted, again, using the Newtonian laws. Newtonian mechanics was so triumphant, that physicists began to believe they had discovered the holly grail of science. This however was all to change, when the same laws were applied to study the behaviour of matter at the smallest scales we knew, the atomic scale.
QUANTUM MECHANICS:
The application of Newtonian mechanics for the study of the atom, after it was discovered by Rutherford that atoms were like minute solar systems, was expected to produce yet more results that would be in agreement with our calculations.  Lo and behold! Things went pare shaped so badly, and it became obvious that new physics was needed urgently. 
We could not explain:
i)  The atomic spectra, 
ii) The black body radiation spectrum
iii)    The photoelectric effect
iv) The wave properties of matter as displayed in the Davisson-Germer experiment.
v)  We could not explain the properties of matter as we were discovering them: Superconductivity, Super fluidity and many more.
All these problems were resolved with just one touch of the strong right hand of quantum mechanics! The new physics was not just a slight modification to Newtonian mechanics, but entirely different and counter intuitive to what we had become accustomed to with Newtonian mechanics. No longer we could talk about objective predictions of how nature was going to behave.  We could only calculate probabilities, and could only talk about probabilities, and we could only predict probabilistically the behaviour of atoms, particles, properties of solids and liquids and so on. 
DO WE COMPROMISE OUR KNOWLEDGE ABOUT NATURE WITH QM?
Views vary on this as it depends on how deeply one is entrenched into the philosophy of Newtonian mechanics.  The point is that, calculation after calculation, observation after observation, nature is telling us that in the micro world matter behaves according to the laws of probability. We might dislike it, but let us think about this for a moment:
Do we really believe, that nature would be able to display the richness of phenomena and variation we observe around us, had the rules she follows been rigid, black and white type of “philosophy,” as we learned from Newtonian mechanics?
We all have our own views on this, so you can form yours.
A: Quantum mechanics, in its essence, is deterministic. It is only measurements that give rise to problems (in the Copenhagen interpretation).
Let's compare three theories: classical mechanics, classical mechanics with random pushing/pulling (stochastical mechanics) and quantum mechanics. In classical mechanics, all laws are deterministic in nature. If $A$ gets you to $B$ and $B$ gets you to $C$, we can easily retrace our steps. We can reverse time and get back to where we started by using the same laws without any problems.
In stochastical mechanics, however, the system we want to describe at random times gets pushed or pulled randomly hard. Let's say you still go from $A$ to $B$ but somewhere between $B$ and $C$ you get a random push in a random direction and you end up in $D$. You can't just retrace your steps. So if we reverse time in stochastical mechanics, we don't necessarily get back to where we started. Determinism is broken.
In quantum mechanics, the laws are again all deterministic in nature. The laws actually look like those of classical mechanics, in an abstract sence. That's to say: $A$ gets you to $B$, $B$ gets you to $C$, maybe $C$ gets you back to $A$, deterministic. It's only measurements that cause us a headache. As long as we don't measure anything, we can simply rewind and nature will get back to its original state. Note the very important difference with stochastical mechanics: quantum mechanics is not just like classical mechanics with a random component!
So QM is deterministic as long as we don't measure anything. However, when we make a measurement (for which a completely satisfying definition doesn't really exist), we can run into problems. Because in the Copenhagen interpretation of QM, a measurement "collapses" the wavefunction, i.e. the system is forced into an eigenstate corresponding to the measuring device. This discontinuity would break determinism. There isn't a general consensus about this among physicists. Some suggest everything is still fine if we describe the measurement fully, including the wavefunctions of all the entities involved in the measurement. Some subscribe to a different interpretation of QM, like the Many-worlds interpretation, where there is no collapse of the wavefunction and therefore no discontinuity either. Others prefer not to think about it too much. (the worst way to go as a scientist in my opinion)
A: It is quite simple actually. 
Quantum mechanics is DETERMINISTIC in the sense of it's laws - they are fixed and are not subject to change. Things which are not deterministic are COORDINATES , which simply means you can not measure well your parameters (but it does not mean, for example, that you can not measure well some combinations of them - like total energy of the system).
Back to your question -- there is no uncertainty of implications in QM there is only uncertainty of position.
