The computer model of the brain
This question's reference to a classical computer refers to a &quot;Turing Machine&quot; style of computation, also known as a knowledge system, in which decisions and possible results are pre-programmed using if-statements, loops, and other logical constructs.
However, most modern computer programmers and engineers are at least somewhat familiar with neural networks, used for machine learning. Artificial neural networks (ANNs) are loosely based on the way the brain (a biological neural network) works.  If you want to use your computing background to understand the brain, then I recommend learning about neural networks instead.  If you already have some understanding of neural networks, then think about how Siri or Watson work.
While neural networks can certainly be thought of as storing data, executing algorithms, parallel processing, and having memory and speed measurements, they are conceptually very different from classical computers, and generally uninstructive to compare. In particular, the &quot;von Neumann&quot; architectural style of modern computers does not have an analog in the brain (there is no separation between areas that compute and areas that store memories, for example). If you are still interested in such a comparison, then many of the questions listed above already have great answers, so check them out.
If you are interested in modeling the brain using a classical computing methodology, then check out ACT-R, a popular architecture for modeling the brain using a modular, knowledge-based system (also see this forum question).
Artificial neural networks are not a perfect model for biological neural networks either, and if you are interested in the difference, then see this forum question.