DNA renaturation is the recombination of two complementary single strands to form a double helix. It is experimentally known that renaturation proceeds through the formation of a double-stranded nucleus of several base pairs (the rate limiting step) followed by a much faster zippering. We consider a lattice polymer model undergoing Rouse dynamics and focus on the nucleation of two diffusing strands. We study numerically the dependence of various nucleation rates on the strand lengths and on an additional local nucleation barrier. When the local barrier is sufficiently high, all renaturation rates considered scale with the length as predicted by Kramers' rate theory and are also in agreement with experiments: their scaling behavior is governed by exponents describing equilibrium properties of polymers. When the local barrier is lowered, renaturation occurs in a regime of genuine non-equilibrium behavior and the scaling deviates from the rate theory prediction.