Re: dead
When you say you checked the cables did you just visually check them?
My red coupe was DOA when it arrived on the transport. Previous owner installed a new battery before he shipped the car because he had issues like you are having. I removed the battery clamps and cleaned inside them and then cleaned the posts. Re-attached clamps and problems were gone.
I agree with MrMmiata. Doesn't sound like the RCM.