Thanks for bringing this issue to our attention via the community. And thanks a lot for the help from @Antoine_Turpin to provide the helpful information.
I regret to hear that you are having problems with your Anker PowerCore+13400 portable chargers. I give our sincere apologies for all the inconvenience caused. From what you've described, it seems the battery is indeed defective. It should be able to be fully recharged in 7-8 hours with a 5V/2A wall adapter and all the LED lights should turn off when it is fully charged.
Be assured that all of our products come with an 18-month warranty. Could you please email us at "firstname.lastname@example.org" to apply for a warranty claim? We can either send you a new replacement or a refund as per your preference. Thanks.