A theoretical analysis of recent experiments measuring the 782 nm surface-enhanced Raman scattering of p-mercaptoaniline bound to silver nanoshells of different core and shell radii [J. B. Jackson and N. J. Halas, Proc. Natl. Acad. Sci. U.S.A. 101, 17930 (2004)] is performed. Electronic structure Hartree-Fock and density-functional theory calculations for Ag salts of p-mercaptoaniline are used to characterize observed vibrational modes and configuration-interaction singles calculations are carried out to examine excited states. Multimode vibronic density-matrix calculations are then made including one excited electronic state, using a classical description of the strong local fields and a phenomenological treatment of relaxations. The spectral behavior as a function of both nanoshell surface-plasmon resonance position and molecular electronic spacing is examined.