An exact and very efficient numerical method for calculating the effective conductivity and local-field distributions in random R-L-C networks is developed. Using this method, the local-field properties of random metal-dielectric films are investigated in a wide spectral range and for a variety of metal concentrations p. It is shown that for metal concentrations close to the percolation threshold (p=p(c)) and frequencies close to the resonance, the local-field intensity is characterized by a non-Gaussian, exponentially broad distribution. For low and high metal concentrations a scaling region is formed that is due to the increasing number of noninteracting dipoles. The local electric fields are studied in terms of characteristic length parameters. The roles of both localized and extended eigenmodes in Kirchhoff's Hamiltonian are investigated.