Powerbank not charging
Your Li-Ion cell is in a very discharged state. When the cell voltage is below 2 V, normal charger would use so-called "pre-charge" mode, trying to charge the cell very slowly, at 20-50-100 mA rate, until its voltage gets up to ~2.5 V. You might need to exercise more patience and wait, monitoring the actual cell voltage. If it doesn't creep up in 20-30 mins, your cell is likely dead. 

Note that even if your power bank would recover eventually, don't expect any good capacity results - overdischarged Li-Ion cells usually suffer unrecoverable loss of capacity, down to nearly zero.