If I discharge my device completely, so that it turns itself off, and then connect the wall charger my device doesn't start blinking immediately. If I let it connected to the charger for some time and then try to boot it, it does work again. So it is charging even if it is not blinking.

So my recommendation would be: connect it to the wall charger for 15 minutes and then disconnect it, boot it and then connect it to the charger again... If it doesn't help - I don't know.

Btw. this is the reason why I never discharge it completely (only close to). And therefor I never turn it off .