Despite considerable study, Saturn's rings continue to challenge current theories for their provenance. Water ice comprises the bulk of Saturn's rings, yet it is the small fraction of non-icy material that is arguably more valuable in revealing clues about the system's origin and age. Herein, we present new measurements of the non-icy material fraction in Saturn's C ring, determined from microwave radiometry observations acquired by the Cassini spacecraft. Our observations show an exceptionally high brightness at near-zero azimuthal angles, suggesting a high porosity of 70-75% for the C ring particles. Furthermore, our results show that most regions in the C ring contain about 1-2% silicates. These results are consistent with an initially nearly pure-ice ring system that has been continuously contaminated by in-falling micrometeoroids over ∼15-90 million years, using the currently accepted value of the micrometeoroid flux at infinity of ∼4.5 × 10-17g cm-2 s-1, and assuming that the C ring optical depth and surface density has not changed significantly during that time. This absolute time scale is inversely proportional not only to the flux at infinity, but also to the amount of gravitational focusing by Saturn the micrometeoroids experience before encountering the rings. We also find an enhanced abundance of non-icy material concentrated in the middle C ring. When assumed to be mixed volumetrically ("intramixed") with water ice, this enhanced contamination reaches a maximum concentration of 6-11% silicates by volume around a ring radius of 83,000 km, depending on the volume mixing model used. This is significantly higher than the inner and outer C ring. As opposed to an intramixing model, we also consider a silicate-core, icy-mantle model to address the fact that silicates may be present in chunks instead of fine powder in the ring particles. Such a model naturally helps to account for the observed opacity distribution. We propose several models to explain the radially varied non-icy material contamination. Our preferred model is that the C ring has been continuously polluted by meteoroid bombardment since it first formed, while the middle C ring was further contaminated by an incoming Centaur, a rocky object torn apart by tides and ultimately broken into pieces that currently reside in the middle C ring. If correct, the spatial extent of the enhanced non-icy material fraction suggests that the Centaur was likely to be captured and integrated into the rings perhaps as recently as ∼10-20 million years ago.