Hmmmmmmmmmmmmmmmmmmmm. ENGINE fan comes on when you turn key to on but it won't engage the starter?
That usually means the PCM/ECU is not fully powered up, this is usually caused by the Engine Control Relay output of the RCM not being there.

Grab the RCM, check every fuse. Two fuses, numbers 2 and 3, are fused outputs of the EC relay. Make sure they are not blown.
Then, I'd pry the RCM open and reconnect it to all plugs - have a helper turn the key to ON. See which relays activate, three should activate, then in about 20 seconds, one relay (the fuel pump relay) will relax.
If you don't get three relays to activate, THAT is your problem. Given it's a new RCM, that would implicate wiring from the key switch to the RCM. But I've not seen that happen before.

ALSO, keep in mind that a weak battery can cause this. If the ECM receives low voltage (not sure how low, around 10.5 I think) it won't fully power up and you get this indication. Swapping batteries from another car will result in the car starting, if it's the battery.

Also, STOP CALLING THE DEALER, you will never get the car going if you rely on a dealer. They will lead you right down the primrose path. Imagine paying $1600 for an ECM and it not fixing anything - it's happened a lot of times before. You cannot condemn the ECM unless you have PROVEN that all inputs to the ECM are good and I doubt they've done that.