First of all, you could simulate all chemistry. Just given the formula, and you could calculate its melting and vaporizing temperatures and other characteristics. After all, chemistry is all particle physics. I guess that can be done even today, to some extent.
Next, you will model a couple million billion particles that are shaped like a vacuum cleaner. This experiment sucks, you think. Let's try something more interesting. You will model a life form - bacteria, and watch the life form fill the memory of your laptop. How nice.
How about modeling a human brain? Let's do it. After all we do have unlimited resources. The brain is modeled, but is very little fun, because you did not model a mouth for it to speak its thoughts. So you don't even know if your brain is conscious. After a short while you get bored of your brain-experiment and stop the simulation, but after doing that, you stop and wonder that did you just kill someone.
You buy some more memory for your computer, as you intend to simulate the entire universe. Now this adding quite a lot of particle x, y and z coordinates and quantum states. As you would like to avoid this, you decide to model the singularity where it all started instead. It will be much easier that way. Your own personal universe starts developing.
Now assuming that the physics of the modeled world correspond to physics of our world, what's the difference between the modeled universe and our universe? Nothing, really.
But there are some requirements to the computer. The computer must be very large. Most likely it should weight more than the system it is modeling. So if it models the state of every particle in the universe, the computer would weight way more than our current universe. Also, the time that it takes for modeling will be at least same than time that is being modeled, which is the age of the universe. The performance of the computer... well, we run out both the prefixes of flops and the Planck constant.
And there is one more limitation. This modeled process should follow the principles of quantum mechanics, to be able to simulate our world. And due to those principles, it is impossible to measure anything without affecting it. If you wanted to really create a model of universe, you should isolate it completely from outside world, to protect our modeled word quantum state from decoherence. You should start the simulation and never have any interaction to it. And that means you will never know if it works or not. Or if you take a peek, you, the modeled universe's Creator, will alter it.
