iPhone 5s won't charge after battery died

I have a iPhone 5s. It was working fine yesterday. The battery was getting low and it wouldn't charge with the cable plugged in. Now, the battery is completely dead. I left it plugged in to the charger all night and it still didn't charge. When I plug it in and push the power button it just keeps telling me to plug in the charger. Did that and it didn't charge. Do I need a new cable? Is there something else I can do?