  We investigate the radio emission of ~185,000 quiescent (optically
unclassifiable) galaxies selected from the Sloan Digital Sky Survey (SDSS). By
median-stacking FIRST cutouts centered on the optically-selected sources, we
are able to reach flux densities down to the 10s of microJy. The quiescent
galaxy sample is composed of two subgroups inhabiting vastly different regimes:
those targeted for the SDSS MAIN Galaxy Sample (~55%), and those targeted for
the Luminous Red Galaxy (LRG) sample (~45%). To investigate the star-formation
rates (SFRs) of these quiescent galaxies, we calibrate a radio-SFR conversion
using a third sample of star-forming galaxies. Comparing this SFR-indicator
with indicators in the optical and UV, we derive conflicting SFR estimates for
the MAIN sample quiescent galaxies. These radio-derived SFRs intersect those
calculated using the 4000-Angstrom break (D4000) around an SFR of 1 Msun/yr and
agree to within a factor of 3 over the range of SFRs. However, we find that the
radio-derived SFRs are too high relative to the SFRs estimated for similar
populations of galaxies using analysis of UV emission, implying either
contamination of the radio by Active Galactic Nuclei (AGN) or incomplete dust
modeling. If AGN activity is dominant in these galaxies, then a relation
between AGN radio luminosity and galaxy mass is required to explain the
observed trends. For the LRGs, on the other hand, we find the radio luminosity
to be independent of SFR as derived from D4000, indicating an AGN component
dominates their radio emission. AGN-based radio emission often implies the
existence of radio jets, providing evidence of a mechanism for low-level
feedback in these quiescent LRGs. (Abridged)
