We use a hybrid density-functional-theory approach to calculate ground-state electronic properties and a time-dependent density-functional-theory approach to investigate the excited state electronic properties of molecular tris-(8-hydroxyquinolate)-aluminum, Alq. The calculated molecular results are compared with measurements on dense solid-state films of Alq. We specifically consider: the optical absorption spectrum near the fundamental absorption threshold, the ionization potential, the single-particle energy gap, the static dielectric constant, and the electric-field dependence of the electron mobility. We find that the molecular calculations can describe the optical absorption spectrum near the fundamental absorption threshold without significant corrections for solid-state effects. The energies of the triplet excited states are computed and the lowest triplet is found to lie 0.64 eV below the lowest excited singlet state. In contrast, large dielectric corrections must be included for the molecular calculations to describe the ionization potential and single-particle energy gap. When these dielectric corrections are made, using the calculated molecular polarizability, which accurately gives the measured static dielectric constant, both the ionization potential and single-particle energy gap are well described. The calculated molecular dipole moment can be used to interpret the electric-field dependence of the electron mobility. The solid-state properties, determined from the molecular calculations, are then used in a device model to describe the measured current-voltage characteristics in Alq diodes.