How to know if the battery is broken

I accidentally drained any last bit of my battery though it took for a while to charge it still managed to work somehow but then suddenly its dead and can't be charge anymore. It can't be factory reset as well. My concern is that, Does my battery just needs to be replaced ? My battery still charges on Universal Charger though and local phone repair shops says my battery is just fine. How to make sure if the battery is completely broken ?