Start by replacing the battery Paul, a known brand of the same or greater amp hour capacity, same dimensions, terminals and orientation. Your present one sounds well past it's sell by date. Ensure new battery is fully charged then start fault finding, if necessary.
ETA: LED lights particularly small warning ones work over a wide voltage range. It could explain therefore why it's illuminated when surrounding electrics and maybe ECU have thrown in the towel.
Last edited by RichardV6; 06/08/21 08:50 AM.