A traditional constant voltage conductivity test method was used to measure how the conductivity of highly insulating low-density polyethylene (LDPE) polymer films depends on applied electric field, repeated and prolonged electric field exposure, and sample temperature. The strength of the applied voltage was varied to determine the electric field dependence. At low electric field, the resistivity was measured from cryogenic temperatures to well above the glass transition temperature. Comparisons were made with a variety of models of the conduction mechanisms common in insulators, including transient polarization and diffusion and steady-state thermally activated hopping conductivity and variable range hopping conductivity, to determine which mechanisms were active for LDPE and to provide a better picture of its electrical behavior.