As energetic particles diffuse out of radio and star-forming galaxies (SFGs), their intracluster density builds up to a level that could account for a substantial part or all the emission from a radio halo. We calculate the particle time-dependent, spectro-spatial distributions from a solution of a diffusion equation with radio galaxies as sources of electrons and SFGs as sources of both electrons and protons. Whereas strong radio galaxies are typically found in the cluster (e.g., Coma) core, the fraction of SFGs increases with distance from the cluster center. Scaling particle escape rates from their sources to the reasonably well determined Galactic rates, and for realistic gas density and magnetic field spatial profiles, we find that predicted spectra and spatial profiles of radio emission from primary and secondary electrons are roughly consistent with those deduced from current measurements of the Coma halo (after subtraction of emission from the relic Coma A). Nonthermal x-ray emission is predicted to be mostly by Compton scattering of electrons from radio galaxies off the CMB, whereas γ-ray emission is primarily from the decay of neutral pions produced in interactions of protons from SFGs with protons in intracluster gas.