It would have been interesting to see if the car started with a key that didn't have a working EWS chip. So you are saying you are back to where you started ??
I had a look through some wiring diagrams but nothing is really clear (and I can't remember) as to if there is another switch for sensing the key or is it just the EWS ring ??
Maybe the ignition switch is not turning off properly and the EWS ring is a bit of a red herring ??
If it really is the EWS ring picking up a signal then you would think it has to be from a chip.
Do you have a scan tool? maybe that can monitor if there is a key present??
You might also try taking the bottom and top covers off just in case there is a chip hiding in there!
Charging doesn't matter for the EWS, only the remote functions.