Hi, there may be at least three issue regarding this symptom.

1. The charger / USB cable is not working
2. the charging port is broken
3. the battery is dead

So how to troubleshoot this problem?

• change to another charger
• change USB cable
• finally if none is working, change the battery. It would cost around USD $20

I've try to use hardware reset / factory reset (press Power button and the Home button simultaneously) but both step fail.

Last option, get a new phone.