In short, yes it can be done but it isn't going to be exactly precise as quantum mechanics goes. People doing research in lattice QCD are doing this very sort of thing; however, the approaches that I've seen have been to program in known laws of physics and use vast amounts of computational power to simulate single particles. Now, this seems a bit counter-intuitive. After all, we see complex simulations all the time using several graphics engines for gaming and the detail of these simulations are becoming quite remarkable.
So back to quantum simulations and in particular quantum entanglement. I'm not going to sit here and argue (As many people like to do) classical physics and the finer points of quantum mechanics equations because I don't believe it's necessary here. There's no point because we're talking about processors that can simulate anything you want with any behavior you desire. Parallelization can simulate two things happening simultaneously communicating with each-other on a classical computer as two sets of instructions can be computed in parallel. As for measurement, since you're the programmer you get to determine what you can and cannot measure.
To my mind this isn't so much of a physics question as it is a programming question depending on what you expect to get out of it. Of course if you have a quantum computer then the methodology changes as there isn't any (Or perhaps only one layer of) abstraction between the physical process and the simulation. As for the actual measurements and/or two computers being separated at a distance, you would probably need a quantum computer (Or two of them) for the kind of precision you'd want but you can still simulate entanglement. I'll give some examples.
This doesn't have to be such a hard problem as in programming simulations. For instance, reference: List of QC_simulators where libraries can be found for simulating quantum entanglement (Just search the page for "Entanglement") in several languages.
I don't see it being non-computable on a classical computer in the sense that the simulation will simulate the quantum mechanical effect but to be clear, you won't actually be entangling two particles on a classical computer and be able to get the same measured results (Bell's inequality does apply here). Sure, you might program your simulation on a classical computer so that the particles are in their proper states but the act of measurement technically won't yield the same results as an actual act of measurement in a real life experiment.
To actually simulate entangled particles you would need a real quantum computer. Otherwise, Bell's inequality, well, wouldn't compute. There are various resources on quantum computing algorithms and programming quantum computers. I haven't researched them that much as I don't have access to a quantum computer but Google has setup a webGL based simulator using the gate method of QC which can be found here: Quantum Computing Playground which I've experimented with and is an interesting resource as are the libraries I previously linked.
In essence, the answer is both yes and no depending on what you're trying to get out of the simulation. Emulating quantum computations isn't like emulating a Nintendo. In that case they're both classical computers.
As a side-note, I would mention that the popular D-Wave computer doesn't use the gate model of quantum computing (Probably why there's been a lot of controversy surrounding their computer) but rather uses adiabatic quantum computing.