on a 172/182 if the immobiliser is armed does it let the fuel pump prime on ignition?
I've had this problem recently and my answer to this is no, it doesn't.
Obviously I'm no mechanic but from my experience with this it only ever primed when the light went out. That's when I knew I could start it.
If anyone is having this problem I highly recommend you replace the two black ignition relays under the bonnet on the right hand side.
New ones only from Renault circa £18 each. I tried swapping them around etc but only when I put new ones in did it fix the issue.
Your barking up the wrong tree with changing batterys in the fob.