Inelastic neutron scattering and Raman scattering spectra of a melt-infiltrated composite of NaAlH4 and active carbon fibers have been measured at low temperature for two sample conditions: as prepared and subjected to hydrogen desorption-absorption cycling. After a careful data analysis, the present experimental results have been compared to the corresponding spectroscopic data taken from bulk NaAlH4 and Na3AlH6. Evident signatures induced by infiltration process onto the NaAlH4 phonon bands have been detected, showing up as a strong peak broadening and smoothing together with, in some cases, an energy shift. Traces of Na3AlH6, appearing as an extra intensity between 130 and 200 meV, seem also confirmed. A substantial agreement between neutron and Raman measurements has been found for the as-prepared melt-infiltrated sample, while for the cycled sample the two techniques produced rather dissimilar results. However, this apparent discrepancy can be explained by considering the different penetration depths of the two spectroscopic probes. Further work, both experimental and based on ab initio simulations, is surely needed in order to rationalize the finding of the present measurements.