iPhone keeps charges and never turns on

Hi everyone,

My mother has an iPhone 5 and started complaining about the battery for a while then the iPhone died. It now shows the low battery symbol with the cable at the bottom, what is shown usually when the battery is dead. When it is connected to power the cable disappears but the low battery symbol stays forever and it never turns on. It is not recognized by iTunes or even the laptop.

Does the problem sound familiar to anyone? My country doesn’t have an Apple Store so I have to troubleshoot this by myself and your help is much appreciated.

Thank you.