iPhone battery does not charge after newly replacing battery (3rd part

My grandmother gave me an iPhone 5S, that she said did not work, didn't hold a charge. I plugged it in and unplugged it, and it showed symptoms of a defective battery. So I replaced the battery, and reset it, but it won't charge. If I plug it into the charger, it recognizes the charger, even tells me its charging, but never charges. So the battery died, and it gives me the, the battery is dead , but it's still charging sign. Help?