The point about old batteries is not so much their remaining capacity in terms of ampere-hours; it is more to do with internal faults that can interfere with the car's ECU. I am no electrician so I can not explain it in any more detail, but I am aware that batteries can suffer internal short circuits, sulphating of the electrodes in lead/acid cells, sediment at the bottom, and other faults that are not apparent to the ordinary user without special test equipment. Can you get the battery tested by an auto electrician? When I last had a new battery fitted as a result of similar false warning lights, loss of turbo, and loss of cruise control, I was told it had to be "coded" to the car. Being a natural cynic, that phrase instantly made me suspicious that I was being told BS. Even though the new battery cured all the problems with the car I still don't know whether to believe this coding story.