When replacing the RCM YOU MUST ONLY PULL ON THE CONNECTORS, not on the wires. Twice now Iv'e seen owners pull on the wires to unplug connectors where they caused intermittent connections in the connectors on the end of the wires.

But also, keep in mind that RCMs are fixable, but they dont always stay fixed.

The easy way out is to put a known-good RCM in and see if that fixes it. I carry a spare RCM, many of us do. Again, the RCM is a KNOWN ISSUE - why do you not have a spare? The no crank implies RCM and the fact you "move things" around the RCM and it starts can imply bad RCM or damage to the connections in the connectors on the RCM wiring.

Replace the RCM with a new one and see what you have, RCMs are cheap, $130 to $180 and are easy to replace - why screw around with what could be a bad RCM? Again, they fail, fixing them is fine, but do not assume a fixed RCM lasts forever, they don't.