Max Tegmark publishes a preprint of a paper arguing from physical principles that consciousness is “what information processing feels like from the inside,” a position I've previously articulated on lesswrong. It's a very physics-rich paper, but here's the most accessable description I was able to find within it:
If we understood consciousness as a physical phenomenon, we could in principle answer all of these questions [about consciousness] by studying the equations of physics: we could identify all conscious entities in any physical system, and calculate what they would perceive. However, this approach is typically not pursued by physicists, with the argument that we do not understand consciousness well enough.
In this paper, I argue that recent progress in neuroscience has fundamentally changed this situation, and that we physicists can no longer blame neuroscientists for our own lack of progress. I have long contended that consciousness is the way information feels when being processed in certain complex ways, i.e., that it corresponds to certain complex patterns in spacetime that obey the same laws of physics as other complex systems, with no "secret sauce" required.
The whole paper is very rich, and worth a read.
Why do you think your computer is not conscious? It probably has more of a conscious experience than, say, a flatworm or sea urchin. (As byrnema notes, conscious does not necessarily imply self-aware here.)