Several young supernova remnants (SNRs) have recently been detected in the high-energy and very-high-energy gamma-ray domains. As exemplified by RX J1713.7-3946, the nature of this emission has been hotly debated, and direct evidence for the efficient acceleration of cosmic-ray protons at the SNR shocks still remains elusive. We analyzed more than 40 months of data acquired by the Large Area Telescope (LAT) on-board the Fermi Gamma-Ray Space Telescope in the HE domain, and gathered all of the relevant multi-wavelength (from radio to VHE gamma-rays) information about the broadband nonthermal emission from RCW 86. For this purpose, we re-analyzed the archival X-ray data from the ASCA/Gas Imaging Spectrometer (GIS), the XMM-Newton/EPIC-MOS, and the RXTE/Proportional Counter Array (PCA). Beyond the expected Galactic diffuse background, no significant gamma-ray emission in the direction of RCW 86 is detected in any of the 0.1-1, 1-10 and 10-100 GeV Fermi-LAT maps. In the hadronic scenario, the derived HE upper limits together with the HESS measurements in the VHE domain can only be accommodated by a spectral index Gamma <= 1.8, i.e. a value in-between the standard (test-particle) index and the asymptotic limit of theoretical particle spectra in the case of strongly modified shocks. The interpretation of the gamma-ray emission by inverse Compton scattering of high energy electrons reproduces the multi-wavelength data using a reasonable value for the average magnetic field of 15-25 muG. For these two scenarios, we assessed the level of acceleration efficiency. We discuss these results in the light of existing estimates of the magnetic field strength, the effective density and the acceleration efficiency in RCW 86.< Leer menos