Scanning tunneling spectroscopy (STS) measurements on highly ordered double layers of the planar organic molecule hexa-peri-hexabenzocoronene (C42H18) on Au(100) are presented and compared to a theoretical characterization of the electronic conductance based on a combination of the Landauer transport formalism with a density-functional-parametrized tight-binding scheme within the local density approximation (LDA). Tunneling spectroscopy data have been recorded within an extended voltage range of +/-2.5 V. In this room temperature STS experiment it was possible to derive not only the energetic positions of the frontier orbitals of a molecular species from tunneling spectroscopy but also the energies of the molecular states next to these frontier orbitals. To achieve a satisfactory agreement between experiment and theory a scaling parameter is necessary which compensates for the underestimation of the electronic energy gap in LDA.