Hey this is most commonly a battery issue. If you left it discharged or did not use it for a while, it is possible that the battery dropped below a threshold voltage. What happens than is the BMS(Battery management system) can prevent the battery from charging as it has dropped below what's considered a safe level. This essentially cuts off the battery from your device, resulting in the symptoms above. Your device will work when plugged in and will commonly show full battery when trying to charge as there will be no battery to charge.

Hey, it could be good to measure the battery voltage. If you left them discharged it is possible that the battery dropped below a threshold voltage. What happens than is the BMS(Battery management system) can prevent the battery from charging as it has dropped below what's considered a safe level. This would align with most of what you have said excluding the fact that the receiver sees those as fully charged , but this could easily be explained as it is possible that since it no longer powers on it could either be reusing the last available data or could be reading the voltage when charging. Either way, the symptoms seem to be very consistent with a dead battery.

This is a ferrite bead not a capacitor. It is used to filter out high frequency noise and it is meant to have a very low resistance and once it fails it tends to actually be an open circuit. As for diagnosis attempt you would have to show some more detailed images and give us some voltage readings. Good luck !

Hey, it depends on whether its not charging or if its not taking a charge. If it is showing that its charging but after unplugging it you see that its not taking charge its very likely to be a battery issue. To solve that you would need to replace the battery(Available for many of the fitbits) but this requires some technical abilities. If its not charging at all there is a vast amount of possibilities of what could be wrong but you could attempt to clean out any debris from the charging connector on both the watch as well as the charger.