Smells like both high parasitic draw (?) and (probably) low quality cell at the same time.
Certain things you say simply don't make sense to me, though. Like “had to be fully charged before use”, for example.
Maybe Banggood knew the unit was faulty, did you got confirmation about this?
Hope the electronics can still work, with some devices the manufacturers set electronic flags which render the devices non-easily restorable. My brother once gave me a 2x AAA powered pop-up trimmer which could work while connected to its power adapter, or if it was turned on connected to the adapter and then disconnected. But the electronics had “discarded” normal operation for the device, and so no way for the stuff to operate without its supply at hand even if their cells were replaced. No way I am buying crap like that, suffice to say.
P.S.: be sure to install a cell with enough power delivery or amperage draw, nothing less than a 30Q I'd recommend.