ECM is the engines computer which is mounted on the drivers side of the eng block. It gets power from the fuse block next to the front of the eng and it gets ground from a bolt that has several wires connected to it at the edge of the quarter panel on the drivers side.
I really think you still have a connection issue. You could trace some of the wires (including grounds) that start from the battery connections and go to other places. check both ends for looseness.
Also, and this is a stretch, do you have a factory security system with coded key? If so then maybe try your other key.