An analysis of the Type Ic supernova (SN) 2004aw is performed by means of models of the photospheric and nebular spectra and of the bolometric light curve. SN2004aw is shown not to be ``broad-lined, contrary to previous claims, but rather a ``fast-lined SN Ic. The spectral resemblance to the narrow-lined Type Ic SN1994I, combined with the strong nebular [O I] emission and the broad light curve, point to a moderately energetic explosion of a massive C+O star. The ejected 56Ni mass is ~0.2 Msun. The ejecta mass as constrained by the models is ~3-5 Msun, while the kinetic energy is estimated as KE ~3-6 e51 ergs. The ratio KE/Mej, the specific energy which influences the shape of the spectrum, is therefore ~1. The corresponding zero-age main-sequence mass of the progenitor star may have been ~23-28 Msun. Tests show that a flatter outer density structure may have caused a broad-lined spectrum at epochs before those observed without affecting the later epochs when data are available, implying that our estimate of KE is a lower limit. SN2004aw may have been powered by either a collapsar or a magnetar, both of which have been proposed for gamma-ray burst-supernovae. Evidence for this is seen in the innermost layers, which appear to be highly aspherical as suggested by the nebular line profiles. However, any engine was not extremely powerful, as the outer ejecta are more consistent with a spherical explosion and no gamma-ray burst was detected in coincidence with SN2004aw.