Still probably a bad relay, or corroded contacts on a relay in the RCM.
Take the cover off with it still connected, make a note of what relays do what when you have someone turn the key : ( the engine control relay in particular, I think the fuel pump relay is OK since you can hear that running )




RCM relays

The TC, air pump and horn relay don't matter at this point.

BTW: check all the RCM fuses with a meter.