But wouldn't it be entirely possible that life would form on a planet where silicone was a predominant element and carbon was extremely rare?
This is what would be necessary. Another possibility is for silicon to beat out carbon in some extremely unusual environments that aren't conducive to silicon based life (IE 'life as we know it').
For example, how about this scenario:
Let's put a planet in orbit around a star. Either the star is cooler than the sun, or comparable to the sun but the planet is farther out. For my example, we'll use a K2 star with a planet that has a semimajor axis of about .65 AU from the star. This planet would be slightly cooler than Mars.
Lets assume this planet is large enough to retain a significant atmosphere and a liquid iron core, which would allow it to have an magnetosphere to protect any forming life. For the purpose of this thought exercise, we'll say this planet is the same size as Earth and contains equal parts silicon and carbon based elements to include a rich, prebiotic environment.
Let's give this planet a moon comparible in size to Luna, but which is only half the distance from the planet as our moon is.
Now, lets assume this planet, which is below the freezing point of water, still has a liquid oceans. The fluid on this planet would likely be a water ammonia mixture. Water/ammonia is capable of functioning as a solvent for life processes, though not as efficiently as pure water. It also remains liquid at much cooler temperatures than pure water.
How would life form on this world?
Well, the obvious answer is that we can't know for sure. It is possible to hypothesize however that on this world, even though there is abundant carbon, any life that arises may actually use silicon as the basis for its life. The reason for this is due to silicon's tendency to form crystal latticework.
I hypothesize that the prebiotic molecules that use the energy from the extremely powerful tidal bores of this world to harness the tidal energy would have an advantage over those who would use stellar energy. As the silicon based molecules form along the tidal basins during the slack tide, they would form extensive crystalline structures that would harness the energy of the incoming tide. The tide would provide them the ability to metabolize nutrients in the water itself to grow and reproduce.
Obviously such life would be autotrophic and very simple. It does however possess the capacity to develop into some very unique forms of life.
It's also entirely possible that there are elements that we haven't discovered yet that could be the basis for life as well.
Honestly, I rather doubt that there are unknown elements of light atomic weight yet to be discovered.