We have obtained new NASA IRTF SpeX spectra of the HR 4796A debris ring system. We find a unique red excess flux that extends out to ~9 um in Spitzer IRS spectra, where thermal emission from cold, ~100K dust from the systems ring at ~75 AU takes over. Matching imaging ring photometry, we find the excess consists of NIR reflectance from the ring which is as red as that of old, processed comet nuclei, plus a tenuous thermal emission component from close-in, T ~ 850 K circumstellar material evincing an organic plus silicate emission feature complex at 7 - 13 um. Unusual, emission-like features due to atomic Si, S, Ca, and Sr were found at 0.96 - 1.07 um, likely sourced by rocky dust evaporating in the 850 K component. An empirical cometary dust phase function can reproduce the scattered light excess and 1:5 balance of scattered vs. thermal energy for the ring with optical depth Tau > 0.10 in an 8 AU wide belt of 4 AU vertical height and Mdust > 0.1-0.7 M_Mars. Our results are consistent with HR 4796A consisting of a narrow sheparded ring of devolatilized cometary material associated with multiple rocky planetesimal subcores, and a small steady stream of dust inflowing from this belt to a rock sublimation zone at approximately 1 AU from the primary. These subcores were built from comets that have been actively emitting large, reddish dust for > 0.4 Myr at 100K, the temperature at which cometary activity onset is seen in our Solar System.