If resoldering the RCM did not work, gotta be the relay itself. You are describing (when you also say the engine fan takes off like a rocket) a failed "engine control relay" output from the RCM.

ONE THING, is it POSSIBLE that the fuse on the RCM feeding the ECM has blown. Make sure all fuses on the RCM are good.
Other than that, I'd almost say what Gary said - order an RCM from FCPEuro. Or send the RCM to DJ and he will ship it back FIXED for $30 - DJ never fails!