We report a comprehensive light element (Li, C, N, O, Na, Mg, and Al) abundance analysis of three solar-type main sequence (MS) dwarfs and three red giant branch (RGB) clump stars in the Hyades open cluster using high-resolution and high signal-to-noise spectroscopy. For each group (MS or RGB), the CNO abundances are found to be in excellent star-to-star agreement. Our results confirm that the giants have undergone the first dredge-up and that material processed by the CN cycle has been mixed to the surface layers. The observed abundances are compared to predictions of a standard stellar model based on the Clemson-American University of Beirut (CAUB) stellar evolution code. The model reproduces the observed evolution of the N and O abundances, as well as the previously derived 12C/13C ratio, but it fails to predict by a factor of 1.5 the observed level of 12C depletion. Li abundances are derived to determine if non-canonical extra mixing has occurred in the Hyades giants. The Li abundance of the giant gamma Tau is in good accord with the predicted level of surface Li dilution, but a ~0.35 dex spread in the giant Li abundances is found and cannot be explained by the stellar model. Possible sources of the spread are discussed; however, it is apparent that the differential mechanism responsible for the Li dispersion must be unrelated to the uniformly low 12C abundances of the giants. Na, Mg, and Al abundances are derived as an additional test of our stellar model. All three elements are found to be overabundant by 0.2-0.5 dex in the giants relative to the dwarfs. Such large enhancements of these elements are not predicted by the stellar model, and non-LTE effects significantly larger (and, in some cases, of opposite sign) than those implied by extant literature calculations are the most likely cause. Comment: 40 pages, 6 figures, 6 tables; accepted by ApJ