When my ring drops off the steering column it dangles on two wires. I put the key in the ignition and everything seems fine but the car won't even try to start. The ignition lights etc seem fine but nothing when I turn the key. This seems similar to the symptoms you are describing which is why I suspect the same cause.
Somewhere the link between the key, the ring and the cars 'brain' there is a break.
You have replaced the key fob battery so we assume that is okay.
Is your ring firmly attached? Mine seems to be a relatively loose push fit which is why it sometimes falls off and how I discovered the issue. Try giving it a wiggle and if that works it suggests a loose wire or connection.
Other than that, I guess your are buggered :-)
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