Interpreting the spectra of brown dwarfs is key to determining the fundamental physical and chemical processes occurring in their atmospheres. Powerful Bayesian atmospheric retrieval tools have recently been applied to both exoplanet and brown dwarf spectra to tease out the thermal structures and molecular abundances to understand those processes. In this manuscript we develop a significantly upgraded retrieval method and apply it to the SpeX spectral library data of two benchmark late T-dwarfs, Gl570D and HD3651B, to establish the validity of our upgraded forward model parameterization and Bayesian estimator. Our retrieved metallicities, gravities, and effective temperature are consistent with the metallicity and presumed ages of the systems. We add the carbon-to-oxygen ratio as a new dimension to benchmark systems and find good agreement between carbon-to-oxygens ratio derived in the brown dwarfs and the host stars. Furthermore, we have for the first time unambiguously determined the presence of ammonia in the low-resolution spectra of these two late T-dwarfs. We also show that the retrieved results are not significantly impacted by the possible presence of clouds, though some quantities are significantly impacted by uncertainties in photometry. This investigation represents a watershed study in establishing the utility of atmospheric retrieval approaches on brown dwarf spectra. ; Comment: submitted to Apj, addressed first round of minor revisions