The local minima or inherent structures (IS) and connected first-order saddles (transition states) are obtained with numerical methods for the N = 32 unit density Lennard-Jones system. Thermodynamic properties of the normal and supercooled liquid states are calculated with the energy distribution of the IS (density of states (DOS)), and approximations for the harmonic and anharmonic vibrational free energy. Different definitions of the configurational entropy, S,, are compared and the Adam-Gibbs relation is found to hold using S, from the IS formalism. The rearrangement pathways between connected neighbor IS are characterized using different measures that are then interpreted with catastrophe theory and the soft potential model. The barrier height distribution is calculated as a function of IS energy, and its relation to the self-diffusion constant, D, and to supercooled dynamics in general, are discussed.